Kinetic layers and coupling conditions for nonlinear scalar equations on networks

被引：11

作者：

Borsche, R. ^{[1
]}

Klar, A. ^{[1
,2
]}

机构：

[1] Tech Univ Kaiserslautern, Dept Math, Erwin Schrodinger Str, D-67663 Kaiserslautern, Germany

[2] Fraunhofer ITWM, Fraunhoferpl 1, D-67663 Kaiserslautern, Germany

来源：

NONLINEARITY | 2018年 / 31卷 / 07期

关键词：

coupling conditions; kinetic layer; kinetic half space problem; Burgers equation; BOUNDARY-VALUE-PROBLEM; CONSERVATION-LAWS; WELL-POSEDNESS; BOLTZMANN-EQUATION; APPROXIMATION; RELAXATION; MODEL; CHEMOTAXIS; JUNCTION; SYSTEM;

D O I：

10.1088/1361-6544/aabc91

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the combination of kinetic half-space problems with Riemann problems at the junction. Detailed numerical comparisons between the different models show the agreement of the coupling conditions for the case of tripod networks.

引用

页数：30

共 34 条

[1] WELL-POSEDNESS OF GENERAL BOUNDARY-VALUE PROBLEMS FOR SCALAR CONSERVATION LAWS [J].