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Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System
- Source :
- Chinese Annals of Mathematics, Series B. 42:135-150
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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 self-similar 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.
- Subjects :
- Conservation law
Equation of state
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Rarefaction
01 natural sciences
Shock (mechanics)
010104 statistics & probability
Nonlinear system
Riemann hypothesis
symbols.namesake
Method of characteristics
symbols
Order (group theory)
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 18606261 and 02529599
- Volume :
- 42
- Database :
- OpenAIRE
- Journal :
- Chinese Annals of Mathematics, Series B
- Accession number :
- edsair.doi...........24493ba45c2c5ac9c8fcd82bf843edec