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

[41] Analysis and approximation of conservation laws with source terms
Greenberg, JM
Leroux, AY
Baraille, R
Noussair, A
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) : 1980 - 2007
[42] The relaxation approximation to hyperbolic system of conservation laws
Hsiao, L
Pan, R
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, VOL 1, 1999, 129 : 485 - 491
[43] Deterministic particle approximation of scalar conservation laws
Di Francesco M.
Fagioli S.
Rosini M.D.
Bollettino dell'Unione Matematica Italiana, 2017, 10 (3) : 487 - 501
[44] CONSERVATION-LAWS AND ANYONS - HARTREE APPROXIMATION
FETTER, AL
HANNA, CB
PHYSICAL REVIEW B, 1992, 45 (05): : 2335 - 2351
[45] Vanishing viscosity approximation to hyperbolic conservation laws
Shen, Wen
Xu, Zhengfu
JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (07) : 1692 - 1711
[46] Nonlocal integrals and conservation laws in the theory of nonlinear solitons
R. I. Bogdanov
Journal of Mathematical Sciences, 2008, 149 (4) : 1400 - 1416
[47] NONLOCAL CONSERVATION-LAWS FOR SUPERSYMMETRIC KDV EQUATIONS
DARGIS, P
MATHIEU, P
PHYSICS LETTERS A, 1993, 176 (1-2) : 67 - 74
[48] Stationary solutions for conservation laws with singular nonlocal sources
Coclite, Giuseppe Maria
Coclite, Mario Michele
JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (02) : 229 - 251
[49] On the accuracy of the finite volume approximations to nonlocal conservation laws
Aggarwal, Aekta
Holden, Helge
Vaidya, Ganesh
NUMERISCHE MATHEMATIK, 2024, 156 (01) : 237 - 271
[50] Conservation laws of the generalized nonlocal nonlinear Schrodinger equation
Ouyang Shi-Gen
Guo Qi
Wu Li-Jun
Lan Sheng
CHINESE PHYSICS, 2007, 16 (08): : 2331 - 2337

← 1 2 3 4 5 →