A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels

被引：0
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作者：
Coclite, Giuseppe Maria [1 ]
Coron, Jean-Michel [2 ]
De Nitti, Nicola [3 ]
Keimer, Alexander [4 ]
Pflug, Lukas [5 ,6 ]
机构：
[1] Department of Mechanics, Mathematics, and Management, Polytechnic University of Bari, Via E. Orabona 4, Bari,70125, Italy
[2] Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu 4, Paris,75252, France
[3] Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, Erlangen,91058, Germany
[4] Institute of Transportation Studies (ITS), University of California Berkeley, Berkeley,CA,94720, United States
[5] Central Institute for Scientific Computing, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 5a, Erlangen,91058, Germany
[6] Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, Erlangen,91058, Germany
来源：
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire | 2023年 / 40卷 / 05期
关键词：
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux; we consider an exponential-type approximation of the Dirac distribution. We then obtain a total variation bound on the nonlocal term and can prove that the (unique) weak solution of the nonlocal problem converges strongly in C.L1loc/ to the entropy solution of the local conservation law. We conclude with several numerical illustrations which underline the main results and; in particular; the difference between the solution and the nonlocal term. © 2022 Association Publications de l’Institut Henri Poincaré;
D O I：
10.4171/AIHPC/58
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页码：1205 / 1223
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