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

作　　者：Gui-Qiang G.Chen 

机构地区：[1]Oxford Centre for Nonlinear PDE,Mathematical Institute,University of Oxford,Oxford OX26GG,UK

出　　处：《Communications on Applied Mathematics and Computation》2023年第3期1015-1052,共38页应用数学与计算数学学报（英文）

基　　金：The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1;the Royal Society-Wolfson Research Merit Award WM090014.

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.

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 

分 类 号：O175[理学—数学]