On approximation of local conservation laws by nonlocal conservation laws

被引：37

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

共 50 条

[31] A numerical scheme for doubly nonlocal conservation laws
Abreu, E.
Valencia-Guevara, J. C.
Huacasi-Machaca, M.
Perez, J.
CALCOLO, 2024, 61 (04)
[32] Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations
Anco, SC
Bluman, G
JOURNAL OF MATHEMATICAL PHYSICS, 1997, 38 (07) : 3508 - 3532
[33] LOCAL CONSERVATION LAWS IN A NONLINEAR ELECTRODYNAMICS
Batsula, O. I.
UKRAINIAN JOURNAL OF PHYSICS, 2011, 56 (05): : 416 - 419
[34] Microcanonical Particlization with Local Conservation Laws
Oliinychenko, Dmytro
Koch, Volker
PHYSICAL REVIEW LETTERS, 2019, 123 (18)
[35] Local variational problems and conservation laws
Ferraris, Marco
Palese, Marcella
Winterroth, Ekkehart
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2011, 29 : S80 - S85
[36] LOCAL SYMMETRIES AND CONSERVATION-LAWS
VINOGRADOV, AM
ACTA APPLICANDAE MATHEMATICAE, 1984, 2 (01) : 21 - 78
[37] CONSTRUCTION OF LOCAL AND NONLOCAL CONSERVATION-LAWS FOR NONLINEAR FIELD-EQUATIONS
VLADIMIROV, VS
VOLOVICH, IV
ANNALEN DER PHYSIK, 1990, 47 (2-3) : 228 - 238
[38] Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms
Rohde, C
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 37 (01) : 103 - 129
[39] Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Coclite, Giuseppe Maria
Colombo, Maria
Crippa, Gianluca
De Nitti, Nicola
Keimer, Alexander
Marconi, Elio
Pflug, Lukas
Spinolo, Laura V.
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2024, 21 (03) : 681 - 705
[40] Analysis and Approximation of Conservation Laws with Source Terms
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, United States
不详
不详
不详
SIAM J Numer Anal, 5 (1980-2007):

← 1 2 3 4 5 →