Mathematical Modelling and Analysis
type: channel
description: Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis. More information ...
publisher: Vilnius Gediminas Technical University
language: en
publication name: Mathematical Modelling and Analysis
issn: 1392-6292
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items: Well-posedness and exponential stability for the logarithmic Lamé system with a time varying delay
items: Numerical algorithms to solve inverse problems for parabolic equations
items: A new closed-form solution for optimal portfolio selection with liquidity risk
items: Re-iterated approximation methods for nonlinear Volterra integral equations
items: Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition
items: Generalized practical stability of Hopfield-type neural networks differential equations
items: Analytical formulas for polynomial coefficients in radial basis function interpolation
items: Weak solutions to degenerate p(t)-Laplacian elliptic equations involving (q, r(t)) double phase Hardy terms
items: On improved P1-interpolation error estimates in W1,p(0, 1): application to the finite element method
items: Variable s-step CGNR method for solving the matrix equation AXB = C arising in image processing
items: On shifts of periodic zeta-function in short intervals
items: Study of a class of nonlinear heterogeneous diffusion with mixed phases under L∞ − data
items: A uniformly accurate hybrid difference approximation of a system of singularly perturbed reaction-diffusion equations with delay using grid equidistribution
items: A second order method for a drug release process defined by a differential Maxwell-Wichert stress-strain relation
items: Approximation of a system of nonlinear Carrier wave equations by approximating the Carrier terms with their integral sums
items: Spectral algorithm for fractional BVPs via novel modified Chebyshev polynomials fractional derivatives
items: Periodic travelling waves of a forced Cahn-Hilliard equation
items: Global existence and uniqueness of mild solution for a fractional Keller-Segel system in Besov-Morrey spaces
items: Robust computing technique for reaction diffusion 2D parabolic problems with shift
items: Convergence analysis of a class of iterative methods: a unified approach
items: Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function
items: A predation model considering a generalist predator and the Rosenzweig functional response
items: One-signed rotationally symmetric solutions of singular Dirichlet problems with the prescribed higher mean curvature operator in Minkowski spacetime
items: Variational analysis of a frictional contact problem with wear and damage
items: A history-dependent frictional contact problem with wear for thermoviscoelastic materials
items: Stability analysis and numerical simulations of IVGTT glucose-insulin interaction models with two time delays
items: A reproducing kernel method for solving singularly perturbed delay parabolic partial differential equations
items: Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions
items: A boundary value problem with an integral condition for a certain fractional differential equation
items: Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions

Well-posedness and exponential stability for the logarithmic Lamé system with a time varying delay
type: item
description: The focus of this paper revolves around the initial–boundary value problem associated with a logarithmic Lamé system within a bounded domain, and incorporating a time-varying delay. We demonstrate the system’s well-posedness through the application of semigroup theory. Subsequently, we establish the existence of global solutions by employing the well-depth method. Furthermore, we establish exponential decay of solutions under adequate constraints concerning the weight of the time-varying delay and the frictional damping.
subject: Articles
  topic: section
subject: logarithmic Lamé system
  topic: keywords
subject: global existence
  topic: keywords
subject: exponential stability
  topic: keywords
subject: nonlinear equations
  topic: keywords
subject: time varying delay
  topic: keywords
creator: Fares Yazid
creator: Salah Mahmoud Boulaaras
creator: Mohammad Shahrouzi
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-02-10
publication date: 2026-02-10
starting page: 194
ending page: 213
doi: 10.3846/mma.2026.24819

Numerical algorithms to solve inverse problems for parabolic equations
type: item
description: This paper presents and analyzes robust numerical algorithms for solving inverse problems for parabolic equations, specifically focusing on the determination of an unknown time-dependent source function from an integral flux condition. The study is motivated by mathematical models based on Navier-Stokes equations, particularly those exhibiting Poiseuille-type solutions. We employ a variational approach, formulating the inverse problem as the minimization of a Tikhonov regularization cost functional. Discrete approximation schemes are rigorously derived using finite volume methods in space and both backward Euler and Crank-Nicolson schemes in time. A key contribution of this work is the strict justification of the gradient formula for the cost functional by deriving the adjoint problem directly from the fully discrete scheme, rather than discretizing the continuous adjoint problem. This methodology is extended to problems involving fractional powers of elliptic operators and two-dimensional domains. Numerical experiments are conducted to compare the efficiency of Gradient Descent and Conjugate Gradient methods. The results demonstrate that the Conjugate Gradient method significantly outperforms standard gradient descent, maintaining high accuracy and convergence rates even with the inclusion of regularization terms and complex diffusion operators.
subject: Articles
  topic: section
subject: inverse problems
  topic: keywords
subject: parabolic partial differential equations
  topic: keywords
subject: Tikhonov regularization
  topic: keywords
subject: adjoint problem
  topic: keywords
subject: gradient-based optimization
  topic: keywords
creator: Raimondas Čiegis
creator: Olga Suboč
creator: Vadimas Starikovičius
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-02-12
publication date: 2026-02-12
starting page: 246
ending page: 266
doi: 10.3846/mma.2026.25585

A new closed-form solution for optimal portfolio selection with liquidity risk
type: item
description: In the literature on optimal portfolio selection problems, it is rare that closed-form solutions are found. It is even more so when liquidity risk needs to be taken into consideration. In this paper, we present a closed-form solution for the optimal weights of a portfolio that consists of a risky and riskless asset under a new key assumption that the liquidity risk is directly proportional to the wealth of the portfolio invested in the risky asset. The solution found is for the Constant Relative Risk Aversion (CRRA) utility function, after successfully solving the associated HJB (HamiltonJacobi-Bellman) equation exactly. Due to the presence of liquidity risk, the research findings reveal that the optimal weights are consistently lower than those found by [19]. Finally, the quantitative impact of the proposed solution is discussed.
subject: Articles
  topic: section
subject: portfolio choice problem
  topic: keywords
subject: log-return assumption
  topic: keywords
subject: liquidity cost
  topic: keywords
subject: closed-form solution
  topic: keywords
creator: Dhruv Goel
creator: Song-Ping Zhu
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-02-11
publication date: 2026-02-11
starting page: 228
ending page: 245
doi: 10.3846/mma.2026.24351

Re-iterated approximation methods for nonlinear Volterra integral equations
type: item
description: In this article, the Newton-iteration scheme based upon iterated Galerkin operator is applied for solving non-linear Volterra Urysohn integral equations of the second kind for smooth and weakly singular kernels. A one step of improvement by iteration to the Galerkin method, named as iterated Galerkin method is a well discussed method and it gives improved convergence rates than Galerkin method. But if we iterate them one more time, then there is no guarantee that we get any improved convergence rates. The proposed Newton-iteration scheme based upon iterated Galerkin operator ensures improved convergence rates at every step of iteration. Specifically, we establish that the convergence rate in iterated Galerkin method increases by O(hr) for smooth kernel, and O(h1−α) for weakly singular kernel, in each step of reiteration, where h is the norm of the partition. Numerical examples are provided to justify the reliability and efficiency of the proposed technique.
subject: Articles
  topic: section
subject: nonlinear Volterra integral equations
  topic: keywords
subject: Newton method
  topic: keywords
subject: smooth kernel
  topic: keywords
subject: weakly singular kernel
  topic: keywords
subject: iterated Galerkin method
  topic: keywords
creator: Samiran Chakraborty
creator: Kapil Kant
creator: Ritu Nigam
creator: Gnaneshwar Nelakanti
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-02-10
publication date: 2026-02-10
starting page: 214
ending page: 227
doi: 10.3846/mma.2026.22594

Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition
type: item
description: This study investigates the steady-state Darcy-Brinkman flow within a thin, saturated porous domain, focusing on the effects of viscous dissipation and non-homogeneous boundary condition for the temperature. Employing asymptotic techniques with respect to the domain’s thickness, we rigorously derive the simplified coupled model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions. The resulting limit model incorporates contributions of viscous dissipation and thermal boundary conditions and thus could prove useful in the engineering applications involving porous media.
subject: Articles
  topic: section
subject: viscous dissipation
  topic: keywords
subject: porous medium
  topic: keywords
subject: non-homogeneous boundary conditions
  topic: keywords
subject: asymptotic modeling
  topic: keywords
creator: Igor Pažanin
creator: Francisco J. Suárez-Grau
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 172
ending page: 193
doi: 10.3846/mma.2026.24073

Generalized practical stability of Hopfield-type neural networks differential equations
type: item
description: This paper investigates the boundedness and practical stability properties of solutions for a class of neural differential equations inspired by Hopfield-type neural networks. Specifically, we develop a novel analytical framework that extends beyond traditional Lyapunov stability theory, Barbalat-type arguments, and fixed-point methods by relaxing common structural assumptions such as smoothness and global Lipschitz continuity. Our approach broadens the class of admissible systems to include nonlinearities with weaker growth conditions and time-varying perturbations that are not easily handled by classical techniques. Sufficient conditions are established to ensure the existence of a globally exponentially stable neighborhood of the origin, even in the presence of varying perturbation conditions. Furthermore, numerical examples are provided to demonstrate and validate the main result.
subject: Articles
  topic: section
subject: equilibrium
  topic: keywords
subject: Hopfield neural networks
  topic: keywords
subject: generalized practical stability
  topic: keywords
subject: boundedness
  topic: keywords
creator: Hanen Damak
creator: Mohamed Ali Hammami
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 149
ending page: 171
doi: 10.3846/mma.2026.23045

Analytical formulas for polynomial coefficients in radial basis function interpolation
type: item
description: Radial basis functions (RBF) are used in many areas, including interpolation and approximation, solution of partial differential equations, neural networks, and machine learning. RBFs are based on the sum of weighted kernel functions. Additional orthogonal polynomials are added for robustness, numerical stability, and computational efficiency improvement. This contribution gives a new analytical formula specifying values of the polynomial coefficients used in RBF interpolation. The zerodegree polynomial coefficient is related to the sigmoid function used in RBF-neural networks (RBF-NN). Unlike prior works where polynomial augmentation is only used to guarantee solvability, this paper provides explicit closed-form formulae for polynomial coefficients (with special focus on the zerodegree case). This new analytical treatment clarifies their role as global bias terms in both interpolation and RBF neural networks. Expected applicability is in data interpolation and approximation, RBF-neural networks, scientific computing and PDE solutions, geostatistics & spatial interpolation, machine learning, and data fitting and signal processing.
subject: Articles
  topic: section
subject: Radial basis functions
  topic: keywords
subject: RBF
  topic: keywords
subject: meshless methods
  topic: keywords
subject: RBF interpolation
  topic: keywords
subject: polynomial
  topic: keywords
subject: RBF neural networks
  topic: keywords
subject: RBF-NN
  topic: keywords
subject: invariance
  topic: keywords
subject: scattered spatio-temporal data
  topic: keywords
creator: Vaclav Skala
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 130
ending page: 148
doi: 10.3846/mma.2026.22788

Weak solutions to degenerate p(t)-Laplacian elliptic equations involving (q, r(t)) double phase Hardy terms
type: item
description: This paper is devoted to establishing novel existence criteria for weak solutions to a class of weighted quasilinear degenerate elliptic equations featuring double phase Hardy-type singular coefficients. These types of problems are rarely discussed in variable exponent Sobolev spaces in previous work. We prove the existence of at least one and at least two weak solutions via variational methods and critical point theory, under appropriate assumptions on the weight function and the nonlinearity.
subject: Articles
  topic: section
subject: weighted Sobolev space
  topic: keywords
subject: degenerate p(t)-Laplacian operators
  topic: keywords
subject: r(t)-Hardy terms
  topic: keywords
subject: variational methods
  topic: keywords
creator: Lili Qi
creator: Jian Liu
creator: Khaled Kefi
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 116
ending page: 129
doi: 10.3846/mma.2026.24048

On improved P1-interpolation error estimates in W1,p(0, 1): application to the finite element method
type: item
description: Based on a new Taylor-like formula, we derived an improved interpolation error estimate in W1,p. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error estimate, derived from the mean value theorem. We then assess the improvement in accuracy we can get from this formula, leading to a significant reduction in finite element computation costs.
subject: Articles
  topic: section
subject: Taylor-like formula
  topic: keywords
subject: error estimates
  topic: keywords
subject: interpolation error
  topic: keywords
subject: approximation error
  topic: keywords
subject: finite elements
  topic: keywords
creator: Joel Chaskalovic
creator: Franck Assous
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 96
ending page: 115
doi: 10.3846/mma.2026.22775

Variable s-step CGNR method for solving the matrix equation AXB = C arising in image processing
type: item
description: The matrix equation $ {AXB} = {C}$ is widely utilized in signal and image processing. In this paper, we present a variable s-step algorithm based on the CGNR method for solving this matrix equation by employing normalization techniques. This algorithm is subsequently enhanced through the application of s-step and regularization methods. By varying the number of basic matrices involved (denoted as s), both the accuracy and speed of the algorithm are improved. The proposed algorithm effectively computes solutions to the matrix equation, demonstrating superior performance when the problem matrices are symmetric. Finally, we investigate the performance and efficacy of these techniques through several numerical examples.
subject: Articles
  topic: section
subject: matrix equation
  topic: keywords
subject: CGNR method
  topic: keywords
subject: variable s-step algorithm
  topic: keywords
subject: regularization method
  topic: keywords
creator: Hojjatollah Shokri Kaveh
creator: Masoud Hajarian
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 79
ending page: 95
doi: 10.3846/mma.2026.23695

On shifts of periodic zeta-function in short intervals
type: item
description: The periodic zeta-function $\zeta(s; a)$, $s = \sigma + it$, $a = \{a_m \in \mathbb{C} : m \in \mathbb{N}\}$, in the half-plane $\sigma > 1$ is defined by Dirichlet series with periodic coefficients $a_m$, and has the meromorphic continuation to the whole complex plane. The function $\zeta(s; a)$ is a generalization of the Riemann zeta-function and Dirichlet $L$-functions. In the paper, using only the periodicity of the sequence $a$, we obtain that the shifts $\zeta(s + i\tau; a)$, $\tau \in \mathbb{R}$, approximate a certain class of analytic functions, defined in the strip $\{s \in \mathbb{C} : 1/2 < \sigma < 1\}$. For $T^{23/70} \leqslant H \leqslant T^{1/2}$, the set of such shifts has a positive lower density in the interval $[T, T + H]$, $T \to \infty$. The case of positive density is also discussed. For the proof, the mean square estimate in short intervals for the Hurwitz zeta-function, and probabilistic limit theorems are applied.
subject: Articles
  topic: section
subject: approximation of analytic functions
  topic: keywords
subject: Dirichlet series
  topic: keywords
subject: Hurwitz zeta-function
  topic: keywords
subject: periodic zeta-function
  topic: keywords
subject: weak convergence
  topic: keywords
creator: Marius Grigaliūnas
creator: Antanas Laurinčikas
creator: Darius Šiaučiūnas
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-21
publication date: 2026-01-21
starting page: 63
ending page: 78
doi: 10.3846/mma.2026.24070

Study of a class of nonlinear heterogeneous diffusion with mixed phases under L∞ − data
type: item
description: In this paper we investigate a class of nonlinear degenerate parabolic equations involving heterogeneous (p,q)-Laplacian operators and subject to Dirichlet boundary conditions. These equations model complex diffusion phenomena with mixed-phase behavior in heterogeneous media. Our aim is to establish existence and uniqueness results for weak solutions under minimal regularity assumptions on the source term f, without requiring any control at infinity. The main difficulties stem from the degeneracy of the operator, the non-standard (p,q)-growth conditions, and the discontinuity of material phases. To overcome these challenges, we develop a variational framework based on Orlicz–Sobolev space theory and employ a generalized version of the Minty–Browder theorem to ensure the surjectivity of the nonlinear operator. Our approach yields new energy estimates, compactness results in non-reflexive settings, and stability under L∞-perturbations of the data. This work provides a rigorous mathematical foundation for analyzing nonlinear diffusion problems in complex and irregular environments.
subject: Articles
  topic: section
subject: double phase operator
  topic: keywords
subject: weak solution
  topic: keywords
subject: existence
  topic: keywords
subject: semi-discretization
  topic: keywords
subject: Rothe’s method
  topic: keywords
subject: weighted Sobolev space
  topic: keywords
creator: El Mehdi Hassoune
creator: Ahmed Jamea
creator: Abdelghali Ammar
creator: Adnane Kaddiri
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-20
publication date: 2026-01-20
starting page: 47
ending page: 62
doi: 10.3846/mma.2026.23889

A uniformly accurate hybrid difference approximation of a system of singularly perturbed reaction-diffusion equations with delay using grid equidistribution
type: item
description: This paper presents a uniformly accurate difference approximation for a system of singularly perturbed reaction-diffusion equations with delay. The proposed method utilizes an appropriate combination of exponential and cubic spline difference schemes. It employs grid equidistribution to address the challenges posed by the multiscale nature of these systems, which often feature sharp gradients and boundary layers. The grid is generated based on the equidistribution of a positive monitor function, a linear combination of a constant floor and a power of the second derivative of the solution. By using adaptive mesh generation and a spline difference method, the approach enhances the accuracy of the numerical solutions while maintaining computational efficiency. Numerical experiments validate the uniform convergence and theoretical findings, demonstrating the method’s robustness irrespective of the perturbation parameter size.
subject: Articles
  topic: section
subject: singular perturbation
  topic: keywords
subject: reaction-diffusion equations
  topic: keywords
subject: adaptive mesh generation
  topic: keywords
subject: spline difference method
  topic: keywords
creator: Aditya Kaushik
creator: Shivani Jain
creator: Manju Sharma
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-19
publication date: 2026-01-19
starting page: 26
ending page: 46
doi: 10.3846/mma.2026.22256

A second order method for a drug release process defined by a differential Maxwell-Wichert stress-strain relation
type: item
description: Polymeric drug delivery platforms offer promising capabilities for controlled drug release thanks to their ability to be custom-designed with specific properties. In this paper we present a model to simulate the complex interplay between solvent absorption, polymer swelling, drug release and stress development within these platforms. A system of nonlinear partial differential equations coupled with an ordinary differential equation is introduced to avoid drawbacks from other models found in the literature. These incorporated a memory effect but from a numerical standpoint, required storing all previous time steps, making them computationally expensive. This paper proposes a new numerical method to simulate such devices based on nonuniform grids and an implicit midpoint time discretization. Our main results are the second order convergence of the method for nonsmooth solutions and the scheme’s stability under the assumption of quasiuniform grids and a small enough timestep.
subject: Articles
  topic: section
subject: drug delivery
  topic: keywords
subject: polymeric devices
  topic: keywords
subject: Maxwell-Wichert
  topic: keywords
subject: numerical method
  topic: keywords
subject: second-order convergence
  topic: keywords
creator: Geovan Campos
creator: José A. Ferreira
creator: Gonçalo Pena
creator: Giuseppe Romanazzi
rights: Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2026-01-19
publication date: 2026-01-19
starting page: 1
ending page: 25
doi: 10.3846/mma.2026.22960

Approximation of a system of nonlinear Carrier wave equations by approximating the Carrier terms with their integral sums
type: item
description: This paper is concerned with the approximation of a system of nonlinear Carrier wave equations (CEs) by approximating the Carrier terms with their integral sums. At first, under suitable conditions, the linear approximate method, the Galerkin method, and compactness arguments provide the unique existence of a weak solution (un,vn) of the problem (Pn), for each n ∈ N, for a system of nonlinear wave equations related to Maxwell fluid between two infinite coaxial circular cylinders. Next, we prove that {(un,vn)}n converges to the weak solution (u,v)of the problem for a system of CEs in a suitable function space. This proof is done by using the compactness lemma of Aubin-Lions and the method of continuity with a priori estimates. We end the paper with a remark related to open problems.
subject: Articles
  topic: section
subject: system of nonlinear wave equations
  topic: keywords
subject: the helical flows of Maxwell fluid
  topic: keywords
subject: Kirchhoff-Carrier equations
  topic: keywords
subject: Faedo-Galerkin method
  topic: keywords
subject: linearization method
  topic: keywords
subject: approximating the Carrier terms
  topic: keywords
creator: Le Thi Phuong Ngoc
creator: Nguyen Vu Dzung
creator: Nguyen Thanh Long
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-04-24
publication date: 2025-04-24
starting page: 362
ending page: 385
doi: 10.3846/mma.2025.22230

Spectral algorithm for fractional BVPs via novel modified Chebyshev polynomials fractional derivatives
type: item
description: This paper introduces a spectral algorithm tailored for solving fractional boundary value problems (BVPs) using the fractional derivatives of modified Chebyshev polynomials. Specifically, it addresses linear and non-linear BVPs and Bratu equations in one dimension via spectral methods. The approach employs basis functions derived from first-kind shifted polynomials that satisfy the homogeneous boundary conditions. The fractional derivatives are formulated to facilitate the solution process. The convergence analysis is studied for the suggested basis expansion; some numerical results are exhibited to verify the applicability and accuracy of the method.
subject: Articles
  topic: section
subject: modified shifted Chebyshev polynomials
  topic: keywords
subject: collocation method
  topic: keywords
subject: Galerkin method
  topic: keywords
subject: fractional BVPs
  topic: keywords
creator: Mohamed Abdelhakem
creator: Dina Abdelhamied
creator: Mamdouh El-kady
creator: Youssri Hassan Youssri
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 714
ending page: 729
doi: 10.3846/mma.2025.22745

Periodic travelling waves of a forced Cahn-Hilliard equation
type: item
description: We prove analytically the existence of a uniparametric family of periodic travelling waves for a Cahn-Hilliard equation with an external forcing term modelling the phase separation of a binary mixture of fluids with thermal diffusion. Some quantitative estimates on the solutions are derived.
subject: Articles
  topic: section
subject: Cahn-Hilliard equation
  topic: keywords
subject: phase separation
  topic: keywords
subject: travelling wave
  topic: keywords
subject: periodic solution
  topic: keywords
subject: a priori estimates
  topic: keywords
creator: Pedro J. Torres
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 707
ending page: 713
doi: 10.3846/mma.2025.23435

Global existence and uniqueness of mild solution for a fractional Keller-Segel system in Besov-Morrey spaces
type: item
description: This paper investigates the fractional Keller-Segel system involving both temporal and spatial variables. We examine fractional dissipation mechanisms for the physical variables, including chemotactic diffusion with fractional dissipation, and incorporate a time-fractional variation in the Caputo sense. Our analysis centers on the fractional heat semigroup, deriving time-decay and integral estimates for Mittag-Leffler operators in Besov-Morrey spaces. Furthermore, we establish a bilinear estimate arising from the nonlinearity of the Keller-Segel system, avoiding reliance on auxiliary norms. These results are then employed to demonstrate the existence and uniqueness of mild solution in Besov-Morrey spaces.
subject: Articles
  topic: section
subject: existence and uniqueness of mild solution
  topic: keywords
subject: Mittag-Leffler operators
  topic: keywords
subject: Besov-Morrey spaces
  topic: keywords
subject: Caputo sense
  topic: keywords
subject: fractional system
  topic: keywords
creator: Hassan Khaider
creator: Mohamed El Ouaarabi
creator: Abderrahmane Raji
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 685
ending page: 706
doi: 10.3846/mma.2025.23324

Robust computing technique for reaction diffusion 2D parabolic problems with shift
type: item
description: Higher dimensional singularly perturbed problems frequently appears in many mathematical modelling. Solving such higher dimensional problem is not as much easy as possible. So order reducing technique namely alternating direction method is one such good choice for solving them. Further singular perturbation problem has its own complexities like boundary and/or interior layers, hence it requires a fitted method on special mesh. Reaction diffusion type singular perturbation problem with space shift is considered in this article. The presence of space shift leads strong interior layer in the solution. To take care of interior and boundary layers, a special mesh is constructed. Hence the problem considered in this article is solved by alternating direction method and fitted difference method with bilinear interpolation. Further the convergence analysis also carried out with rate one in both time and space. Computational validation is also done.
subject: Articles
  topic: section
subject: ADI method
  topic: keywords
subject: 2-D parabolic problems
  topic: keywords
subject: bilinear interpolation
  topic: keywords
subject: reaction diffusion equation
  topic: keywords
creator: Veerasamy Subburayan
creator: Srinivasan Natesan
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 664
ending page: 684
doi: 10.3846/mma.2025.21517

Convergence analysis of a class of iterative methods: a unified approach
type: item
description: In this paper, we study the convergence of a class of iterative methods for solving the system of nonlinear Banach space valued equations. We provide a unified local and semi-local convergence analysis for these methods. The convergence order of these methods are obtained using the conditions on the derivatives of the involved operator up to order 2 only. Further, we provide the number of iterations required to obtain the given accuracy of the solution. Various numerical examples including integral equations and Caputo fractional differential equations are considered to show the performance of our methods.
subject: Articles
  topic: section
subject: iterative methods
  topic: keywords
subject: nonlinear equations
  topic: keywords
subject: Caputo fractional operator
  topic: keywords
subject: basin of attraction
  topic: keywords
creator: Muniyasamy Murugan
creator: Chandhini Godavarma
creator: Santhosh George
creator: Indra Bate
creator: Kedarnath Senapati
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 645
ending page: 663
doi: 10.3846/mma.2025.21979

Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function
type: item
description: This paper presents a novel 6D dynamic system derived from modified second-type 3D Lorenz equations using state feed- back control. While these original 3D equations are structurally simpler than the classical Lorenz equations, they generate more topologically complex attractors with a distinctive two-winged butterfly structure. The proposed system is the most compact of its kind in the literature, containing only 11 terms: two cross-product nonlinearities, two piecewise linear functions, one cosine function, five linear terms, and one constant. The newly developed 6D hyper- chaotic system exhibits rich dynamic properties, including hidden attractors and dissipative behavior. A detailed dynamic analysis has identified two unstable hyperbolic equilibrium points, indicating the potential for self-exciting attractors. Additionally, bifurcation diagrams were constructed, Lyapunov exponents were computed, and the maximum Kaplan-Yorke dimension DKY = 3.23 was obtained at parameter value a = 0.5, revealing the high complexity of the hyperchaotic dynamics. Furthermore, multistability and offset boosting control were examined to gain deeper insights into the system’s behavior. Finally, synchronization between two identical 6D hyperchaotic systems was successfully achieved using an adaptive control method.
subject: Articles
  topic: section
subject: two-wing attractors
  topic: keywords
subject: chaotic behavior
  topic: keywords
subject: multistability
  topic: keywords
subject: offset boosting control
  topic: keywords
subject: adaptive synchronization
  topic: keywords
creator: Michael Kopp
creator: Inna Samuilik
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-11
publication date: 2025-11-11
starting page: 626
ending page: 644
doi: 10.3846/mma.2025.23438

A predation model considering a generalist predator and the Rosenzweig functional response
type: item
description: This work deals with the dynamics of an ordinary differential equation system describing a Leslie-Gower predator-prey model with a generalist predator and a non-differentiable functional response proposed by M. L. Rosenzweig, given by h(x) = qxα with 0 < α < 1. Two aspects have a significant impact on the model: (1) the predator’s carrying capacity depends on both the favorite prey population and an alternative food source, and (2) consumers have access to an alternative food source. Among the main results, a separatrix curve Σ arises dividing the phase plane into regions with different dynamic behaviors. Trajectories above the separatrix curve Σ reach the vertical axis in finite time, while those below Σ may converge to positive equilibrium points, limit cycles, or homoclinic connections. Furthermore, the system is non-Lipschitz, implying non-uniqueness of solutions at points of the vertical axis. Several bifurcations, including saddle-node, homoclinic, Hopf, generalized Hopf, and Bogdanov-Takens bifurcations, are identified through the use of computational techniques. The dynamics of the system are visualized by presenting a bifurcation diagram in a convenient parameter space.
subject: Articles
  topic: section
subject: predator-prey model
  topic: keywords
subject: Leslie-Gower model
  topic: keywords
subject: separatrix
  topic: keywords
subject: bifurcations
  topic: keywords
subject: limit cycles
  topic: keywords
subject: homoclinic connection
  topic: keywords
creator: Viviana Rivera-Estay
creator: Alejandro Rojas-Palma
creator: Eduardo González-Olivares
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 604
ending page: 625
doi: 10.3846/mma.2025.22892

One-signed rotationally symmetric solutions of singular Dirichlet problems with the prescribed higher mean curvature operator in Minkowski spacetime
type: item
description: We investigate the existence, uniqueness and multiplicity of one-signed rotationally symmetric solutions of singular Dirichlet problems with the prescribed higher mean curvature operator in Minkowski spacetime. The main tools are the Schauder fixed point theorem along with cut-off technique and the Leggett-Williams fixed point theorem. In addition, we give some practical models to illustrate the effectiveness of our results.
subject: Articles
  topic: section
subject: higher mean curvature operator
  topic: keywords
subject: Minkowski spacetime
  topic: keywords
subject: singular Dirichlet problem
  topic: keywords
subject: one-signed rotationally symmetric solutions
  topic: keywords
creator: Meiyu Liu
creator: Minghe Pei
creator: Libo Wang
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 583
ending page: 603
doi: 10.3846/mma.2025.23218

Variational analysis of a frictional contact problem with wear and damage
type: item
description: We study a quasistatic problem describing the contact with friction and wear between a piezoelectric body and a moving foundation. The material is modeled by an electro-viscoelastic constitutive law with long memory and damage. The wear of the contact surface due to friction is taken into account and is described by the differential Archard condition. The contact is modeled with the normal compliance condition and the associated law of dry friction. We present a variational formulation of the problem and establish, under a smallness assumption on the data, the existence and uniqueness of the weak solution. The proof is based on arguments of parabolic evolutionary inequations, elliptic variational inequalities and Banach fixed point.
subject: Articles
  topic: section
subject: quasistatic process
  topic: keywords
subject: electro-viscoelastic materials
  topic: keywords
subject: damage
  topic: keywords
subject: normal compliance
  topic: keywords
subject: friction
  topic: keywords
subject: wear
  topic: keywords
subject: existence and uniqueness
  topic: keywords
subject: fixed point arguments
  topic: keywords
subject: weak solution
  topic: keywords
creator: Mohammed Salah Mesai Aoun
creator: Mohamed Selmani
creator: Abdelaziz Azeb Ahmed
rights: Copyright (c) 2021 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2021-05-26
publication date: 2021-05-26
starting page: 170
ending page: 187
doi: 10.3846/mma.2021.11942

A history-dependent frictional contact problem with wear for thermoviscoelastic materials
type: item
description: In this manuscript we study a contact problem between a deformable viscoelastic body and a rigid foundation. Thermal effects, wear and friction between surfaces are taken into account. A variational formulation of the problem is supplied and an existence and uniqueness result is proved. The idea of the proof rested on a recent result on history-dependent quasivariational inequalities. Finally, a perturbation of the data is initiated and a convergence result is demonstrated when the perturbation parameter converges to zero.
subject: Articles
  topic: section
subject: viscoelastic material
  topic: keywords
subject: thermal effects
  topic: keywords
subject: friction
  topic: keywords
subject: history-dependent quasivariational inequality
  topic: keywords
subject: convergence result
  topic: keywords
creator: Lamia Chouchane
creator: Lynda Selmani
rights: Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University. https://creativecommons.org/licenses/by/4.0
date: 2019-04-19
publication date: 2019-04-19
starting page: 351
ending page: 371
doi: 10.3846/mma.2019.022

Stability analysis and numerical simulations of IVGTT glucose-insulin interaction models with two time delays
type: item
description: This paper presents a systematic study of a mathematical model of glucose and insulin interaction with two time delays, with a focus on analytical studies, bifurcation analysis, and very well numerical simulations. This model based on the Intra-Venous Glucose Tolerance Test (IVGTT) and is presented with two time delays. One delay is the insulin response time to an increase in glucose concentration, and the hepatic glucose production time delay is the other. Then, we establish results on positivity, boundedness, and persistence. We also provide suﬃcient stability analysis conditions for both local and global asymptotic stability of the proposed models. For the latter, two diﬀerent strategies are used: stability bifurcation analysis and Lyapunov-Krasovskii functionals. We investigate diﬀerent regions of parameter space using two approaches, that yield diﬀerent sets of suﬃcient conditions for global stability. The bifurcation graphs generated from our extensive and carefully designed simulations complement and conﬁrm these analytical results. The insulin concentration level peaks after the glucose concentration level, according to the numerical simulations.
subject: Articles
  topic: section
subject: glucose-insulin regulatory system
  topic: keywords
subject: insulin secretion
  topic: keywords
subject: ultradian oscillation
  topic: keywords
subject: delay diﬀerential equation model
  topic: keywords
creator: Sayed Saber
creator: Ahmad Alalyani
rights: Copyright (c) 2022 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2022-08-12
publication date: 2022-08-12
starting page: 383
ending page: 407
doi: 10.3846/mma.2022.14007

A reproducing kernel method for solving singularly perturbed delay parabolic partial differential equations
type: item
description: In this article, we put forward an efficient method on the foundation of a few reproducing kernel spaces(RK-spaces) and the collocation method to seek the solution of delay parabolic partial differential equations(PDEs) with singular perturbation. The approximated solution to the equations is formulated and proved the exact solution is uniformly convergent by the solution. Furthermore, the partial differentiation of the approximated solution is also proved the partial derivatives of the exact solution is uniformly convergent by the solution. Meanwhile, we show that the accuracy of our method is in the order of T/n where T is the final time and n is the number of spatial (and time) discretization in the domain of interests. Three numerical examples are put forward to demonstrate the effectiveness of our presented scheme.
subject: Articles
  topic: section
subject: delay parabolic equation
  topic: keywords
subject: reproducing kernel method
  topic: keywords
subject: collocation method
  topic: keywords
subject: numerical solution
  topic: keywords
creator: Ruifeng Xie
creator: Jian Zhang
creator: Jing Niu
creator: Wen Li
creator: Guangming Yao
rights: Copyright (c) 2023 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2023-09-04
publication date: 2023-09-04
starting page: 469
ending page: 486
doi: 10.3846/mma.2023.16852

Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions
type: item
description: This introduces a new method that effectively solves spatiotemporal fractional diffusion equation(FDE) using fractional Lagrange interpolation and fractional multiwavelets. The method effectively addresses situations with non-smooth solutions. The approach begins by discretizing the time variable t using the fractional piecewise parabolic Lagrange interpolation method. For the spatial variables, we construct fractional multiwavelets. Through the least residue method, we obtain approximate solutions, while also conducting convergence analysis. Numerical demonstrations validate the high accuracy achieved by the proposed method, notably showcasing the better approximation capability of fractional polynomials compared to their integer counterparts.
subject: Articles
  topic: section
subject: fractional calculus
  topic: keywords
subject: fractional diffusion equation
  topic: keywords
subject: least residue method
  topic: keywords
subject: fractional multiwavelets
  topic: keywords
creator: Jian Zhang
creator: Chaoyue Guan
creator: Hong Du
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-07-03
publication date: 2025-07-03
starting page: 421
ending page: 438
doi: 10.3846/mma.2025.22650

A boundary value problem with an integral condition for a certain fractional differential equation
type: item
description: The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a priori estimate is established for the associated problem. Secondly, the density of the operator range generated by the considered problem is proved by using the functional analysis method.
subject: Articles
  topic: section
subject: energy inequality
  topic: keywords
subject: fractional differential equation
  topic: keywords
subject: Caputo derivatives
  topic: keywords
subject: integral boundary conditions
  topic: keywords
subject: strong solution
  topic: keywords
creator: Bouthina Sabah Hammou
creator: Abdelkader Djerad
creator: Ameur Memou
creator: Chahla Latrous
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-07-03
publication date: 2025-07-03
starting page: 405
ending page: 420
doi: 10.3846/mma.2025.21481

Analysis study of hybrid Caputo-Atangana-Baleanu fractional pantograph system under integral boundary conditions
type: item
description: This manuscript investigates the qualitative analysis of a new hybrid fractional pantograph system involving AtanganaBaleanu-Caputo derivatives, complemented by hybrid integral boundary conditions. Dhage’s fixed point theorem is employed to investigate the existence theorem of the solutions, while uniqueness is proven by using Perov’s approach and Lipschitz’s matrix. The Hyers-Ulam (HU) stability is also demonstrated using the Lipschitz’s matrix and techniques from nonlinear analysis. Finally, illustrative example is enhanced to examine the effectiveness of the obtained results.
subject: Articles
  topic: section
subject: Caputo-Atangana-Baleanu operator
  topic: keywords
subject: coupled hybrid fractional differential system
  topic: keywords
subject: pantograph problem
  topic: keywords
subject: Dhage and Perov techniques
  topic: keywords
subject: Lipschitzian’s matrix
  topic: keywords
creator: Sabri T. M. Thabet
creator: Imed Kedim
creator: Mohammad Esmael Samei
creator: Thabet Abdeljawad
rights: Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0
date: 2025-04-24
publication date: 2025-04-24
starting page: 386
ending page: 404
doi: 10.3846/mma.2025.22328