Singular Structure Of Global Solution For A Class Of Two-Dimensional Conservation Laws

In this paper, we investigate two-dimensional Riemann problem of simplified Euler equation, where its initial data just contains two constant states separated by a smooth curve. We propose a new approach to construct a two-dimensional global solution, which is different from usual self-similar solution. Some new properties of two-dimensional wave are also discovered.The paper is divided into four parts.In the first part, we introduce the background of the two-dimensional simplified Euler equation and the relating research progress.In the second part, we give some important definitions about the two-dimensional simplified Euler equation. Furthermore, we construct the two-dimensional elementary wave of this equation and discuss their properties preliminarily.In the third part, by studying the two-dimensional elementary wave in a further step, we find that the two-dimensional elementary wave which connects left state and intermediate state is contact discontinuity. The possible two-dimensional elementary wave that connects intermediate state and right state is either 2-th rarefaction or 2-th shock wave. From the results above, we can construct intermediate solution.Finally, we can construct the new structure of the global solution of two-dimensional simplified Euler equation and find singular structure of global solution.