On approximation of local conservation laws by nonlocal conservation laws

被引：34

作者：

Keimer, Alexander ^{[1
]}

Pflug, Lukas ^{[2
]}

机构：

[1] Univ Calif Berkeley, ITS, Berkeley, CA 94720 USA

[2] Friedrich Alexander Univ Erlangen Nurnberg FAU, Dept Math, Chair Appl Math 2, Cauerstr 11, D-91058 Erlangen, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 475卷 / 02期

关键词：

Nonlocal balance laws; Convergence of the nonlocal model to corresponding local model; Entropy solution; Traffic flow modelling; LWR PDE; TRAFFIC FLOW MODEL; BALANCE LAWS; UNIQUENESS; EXISTENCE; SYSTEM; REGULARITY; WAVES;

D O I：

10.1016/j.jmaa.2019.03.063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for monotone initial datum the solution of nonlocal conservation laws converges to the entropy solution of the corresponding local conservation laws when the nonlocal reach tends to zero. This particularly covers the principle cases of conservation laws: shocks and rarefactions. The considered problem is addressed by studying the Entropy of the nonlocal conservation laws in the limit and by exploiting the semi-explicit solution formula developed in [30]. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1927 / 1955

页数：29

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