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

被引：10

作者：

Coclite, Giuseppe Maria ^{[1
]}

Coron, Jean-Michel ^{[2
]}

De Nitti, Nicola ^{[3
]}

Keimer, Alexander ^{[4
]}

Pflug, Lukas ^{[5
,6
]}

机构：

[1] Polytech Univ Bari, Dept Mech Math & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Paris 06, Lab Jacques Louis Lions, Pl Jussieu 4, F-75252 Paris, France

[3] Friedrich Alexander Univ Erlangen Nurnberg, Dept Data Sci, Cauerstr 11, D-91058 Erlangen, Germany

[4] Univ Calif Berkeley, Inst Transportat Studies ITS, Berkeley, CA 94720 USA

[5] Friedrich Alexander Univ Erlangen Nurnberg, Cent Inst Sci Comp, Martensstr 5a, D-91058 Erlangen, Germany

[6] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2023年 / 40卷 / 05期

关键词：

Nonlocal conservation laws; nonlocal flux; balance laws; singular limits; approximation of local conservation laws; entropy solution; TRAFFIC FLOW MODEL; BALANCE LAWS; UNIFORM CONTROLLABILITY; TRANSPORT-EQUATION; UNIQUENESS; EXISTENCE; REGULARITY; SYSTEM; CONVERGENCE; STABILITY;

D O I：

10.4171/AIHPC/58

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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(L-loc(1)) 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.

引用

页码：1205 / 1223

页数：19

共 62 条

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