Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems

被引：0
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作者：
Gui-Qiang G. Chen
机构：
[1] University of Oxford,Oxford Centre for Nonlinear PDE, Mathematical Institute
来源：
Communications on Applied Mathematics and Computation | 2023年 / 5卷
关键词：
Riemann problems; Two-dimensional (2-D); Transonic shocks; Solution structure; Free boundary problems; Mixed elliptic-hyperbolic type; Global configurations; Large-time asymptotics; Global attractors; Multidimensional (M-D); Shock capturing methods; Primary: 35L65; 35L67; 35M10; 35M30; 35R35; 76N10; 35B36; 35D30; 76H05; 76J20; Secondary: 35B30; 35B40; 76N30; 65M08; 76L05;
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学科分类号：
摘要：
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional (2-D) Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
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页码：1015 / 1052
页数：37
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