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

Citation:

Geng LAI,Sisi XIE.Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System[J].Chinese Annals of Mathematics B,2021,42(1):135~150
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Authors:

Geng LAI; Sisi XIE

Foundation:

This work was supported by the National Natural Science Foundation of China (No.,11301326).
Abstract: In order to construct global solutions to two-dimensional (2D 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 2D 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 2D 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 2D Riemann problems.

Keywords:

Nonlinear wave system, Rarefaction wave, Shock-rarefaction composite wave, Wave interaction, Characteristic decomposition

Classification:

35L65, 35L67.
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