Envelope and classification of global structures of solutions for a class of two-dimensional conservation laws

Abstract

Two-dimensional Riemann problem for scalar conservation law are investigated and classification of global structure for its non-selfsimilar solution is given by analysis of structure and classification of envelope for non-selfsimilar 2D rarefaction wave. Initial data has two different constant states which are separated by initial discontinuity. We propose the concepts of plus envelope, minus envelope and mixed envelope, and some new structures and evolution phenomena are discovered by use of these concepts.