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.
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.
作者简介
Gui-Qiang G.Chen,chengq@maths.ox.ac.uk。
