The Interaction And Evolution Of Elementary Waves For Multi-Dimensional Conservation Laws

In this thesis, the multi-dimensional Riemann problems are discussed, inwhich initial discontinuity is a sphere.We will investigate the interaction between multi-dimensional elementarywaves, their global structure and evolution of global solutions. We discoversome new phenomena which are essential di?erent from the one-dimensionalcase. The analytic solution we get can be treated as the standard solution bywhich di?erent numerical schemes can be verified.This thesis is composed by three chapters.The first chapter is introduction which some background and importanceof our topic are introduced.The second chapter is the presentation of our problem and the discussionof global analytic solution for the case of u_- < u_+.The third chapter is the discussion of global analytic solution for the caseof u_- > u_+.