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On the Dirichlet-Neumann Boundary Problem for Scalar Conservation Laws

    Marin Mišur Affiliation
    ; Darko Mitrovic Affiliation
    ; Andrej Novak Affiliation

Abstract

We consider a Dirichlet-Neumann boundary problem in a bounded domain for scalar conservation laws. We construct an approximate solution to the problem via an elliptic approximation for which, under appropriate assumptions, we prove that the corresponding limit satisfies the considered equation in the interior of the domain. The basic tool is the compensated compactness method. We also provide numerical examples.

Keyword : scalar conservation law, bounded domain, Dirichlet-Neumann problem, compensated compactness, numerical simulations

How to Cite
Mišur, M., Mitrovic, D., & Novak, A. (2016). On the Dirichlet-Neumann Boundary Problem for Scalar Conservation Laws. Mathematical Modelling and Analysis, 21(5), 685-698. https://doi.org/10.3846/13926292.2016.1214187
Published in Issue
Sep 20, 2016
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This work is licensed under a Creative Commons Attribution 4.0 International License.