Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System  

作　　者：Geng LAI Sisi XIE 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Chinese Annals of Mathematics,Series B》2021年第1期135-150,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11301326)。

摘　　要：In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.

关 键 词：Nonlinear wave system Rarefaction wave Shock-rarefaction composite wave Wave interaction Characteristic decomposition 

分 类 号：O175.27[理学—数学]