Conservation laws with discontinuous flux: a short introduction

被引：0
作者：
Raimund Bürger
Kenneth H. Karlsen
机构：
[1] Universidad de Concepción,Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas
[2] University of Oslo,Centre of Mathematics for Applications (CMA)
来源：
Journal of Engineering Mathematics | 2008年 / 60卷
关键词：
Conservation laws; Discontinuous flux; Numerical methods; Transport equations; Well-posedness analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Conservation laws with discontinuous flux have attracted recent attention both due to their numerous applications and the intriguing theoretical challenges raised by their well-posedness and numerical analysis. This introductory note states the basic problem considered in the eight contributions of this Special Issue. Three different types of applications are surveyed where these equations appear, motivated by spatially heterogeneous physical models, adjoint problems for parameter identification, and numerical methods for systems of conservation laws, respectively. Basic problems arising in the analysis of these equations are discussed, and the contributions of the Special Issue are presented.
引用
收藏
页码：241 / 247
页数：6
相关论文
共 58 条
[1]  
Lighthill MJ(1955)On kinematic waves. II. A theory of traffic flow on long crowded roads Proc Roy Soc London Ser A 229 317-345
[2]  
Whitham GB(1956)Shock waves on the highway Oper Res 4 42-51
[3]  
Richards PI(1987)An analysis of the traffic on highways with changing surface conditions Math Model 9 1-11
[4]  
Mochon S(1990)What does the entropy condition mean in traffic flow theory? Transp Res B 24B 133-143
[5]  
Ansorge R(1999)Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium Comput Geosci 3 23-48
[6]  
Kaasschieter EF(1995)Effects of capillary forces on immiscible two-phase flow in strongly heterogeneous porous media Transp Porous Media 21 71-93
[7]  
Van Duijn CJ(2005)Closed-form and finite difference solutions to a population balance model of grinding mills J Eng Math 51 165-195
[8]  
De Neef MJ(2005)Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials Comm Math Sci 3 285-315
[9]  
Molenaar J(1988)Two new moving boundary problems for scalar conservation laws Comm Pure Appl Math 41 725-737
[10]  
Bürger R(1999)A free boundary problem for scalar conservation laws SIAM J Math Anal 30 985-1009
123456