Mathematical Modelling and Analysis

Joint discrete approximation of analytic functions by shifts of Lerch zeta-functions

Antanas Laurinčikas — 2024-03-26

The Lerch zeta-function depends on two real parameters λ and and, for σ > 1, is defined by the Dirichlet series , and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts with arbitrary 1 and We prove that there exists a non-empty closed set of analytic functions on the critical strip which is approximated by the above shifts. It is proved that the set of shifts approximating a given collection of analytic functions has a positive lower density. The case of positive density also is discussed. A generalization for some compositions is given.

Simultaneous inversion of the source term and initial value of the time fractional diffusion equation

Fan Yang — 2024-03-26

In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.

Topographical effects on wave scattering by an elastic plate floating on two-layer fluid

Ramanababu Kaligatla — 2024-03-26

This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.

Identification of a time-dependent source term in a nonlocal problem for time fractional diffusion equation

Mansur I. Ismailov — 2024-03-26

This paper is concerned with the inverse problem of recovering the time dependent source term in a time fractional diffusion equation, in the case of nonlocal boundary condition and integral overdetermination condition. The boundary conditions of this problem are regular but not strongly regular. The existence and uniqueness of the solution are established by applying generalized Fourier method based on the expansion in terms of root functions of a spectral problem, weakly singular Volterra integral equation and fractional type Gronwall’s inequality. Moreover, we show its continuous dependence on the data.

The dirichlet problem for a class of anisotropic Schrödinger-Kirchhoff-type equations with critical exponent

Nabil Chems Eddine — 2024-03-26

In this paper, our focus lies in addressing the Dirichlet problem associated with a specific class of critical anisotropic elliptic equations of Schrödinger-Kirchhoff type. These equations incorporate variable exponents and a real positive parameter. Our objective is to establish the existence of at least one solution to this problem.

Some considerations on numerical methods for Cauchy singular integral equations on the real line

Maria Rosaria Capobianco — 2024-03-26

Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.

Comparative analysis of models of genetic and neuronal networks

Diana Ogorelova — 2024-03-26

The comparative analysis of systems of ordinary differential equations, modeling gene regulatory networks and neuronal networks, is provided. In focus of the study are asymptotical behavior of solutions, types of attractors. Emphasis is made on the chaotic behavior of solutions.

The global strong solutions of the 3D incompressible Hall-MHD system with variable density

Shu An — 2024-03-26

In this paper, we focus on the well-posedness problem of the three-dimensional incompressible viscous and resistive Hall-magnetohydrodynamics system (Hall-MHD) with variable density. We mainly prove the existence and uniqueness issues of the density-dependent incompressible Hall-magnetohydrodynamic system in critical spaces on .

Investigation of a discrete Sturm–Liouville problem with two-point nonlocal boundary condition and natural approximation of a derivative in boundary condition

Kristina Bingelė — 2024-03-26

The article investigates a discrete Sturm–Liouville problem with one natural boundary condition and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures.

A discrete version of the Mishou theorem related to periodic zeta-functions

Aidas Balčiūnas — 2024-03-26

In the paper, we consider simultaneous approximation of a pair of analytic functions by discrete shifts and of the absolutely convergent Dirichlet series connected to the periodic zeta-function with multiplicative sequence a, and the periodic Hurwitz zeta-function, respectively. We suppose that and as and the set is linearly independent over

A modified Newton-secant method for solving nonsmooth generalized equations

Vitaliano de Sousa Amaral — 2024-03-26

In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.

A Singular nonlinear problems with natural growth in the gradient

Boussad Hamour — 2024-03-26

In this paper, we consider the equation with boundary conditions where is an open bounded subset of is a Leray-Lions operator defined on is a characteristic function, and is a Carathéodory function such thatsign Forand sufficiently small, we prove the existence of at least one solution u of this problem which is moreover such that the function belongs tofor some This solution satisfies some a priori estimates in