Un-selfsimilar Elementary Wave and Global Solutions of a Class of Multi-dimensional Conservation Laws

摘要

@@ 1 Introduction and Main ResultsrnFor Riemann problem in n(n ≥ 3) dimensional(n-D) conservation laws, dimension of equations can beonly reduced one dimension by applying self-similar approach, so transformed equations are at least two dimensional (2D) equations which are also very hard although some pioneer works have been done in References [1-3]. Additionally as generalization of Riemann data, n-D Riemann data are set as constant states in different octants under self-silimar transformation,so many complicated cases of wave interacton will happen. So except some symmetric situations that can be reduced to one dimensional cases, there are rare theoretical results for n-D conservation laws.