The Summary To The Generalized Riemann Problem For A Class Of Hyperbolic Systems Of Conservation Laws

The partial differential equation is an important method for people to explore the phenomenon and laws in nature. As a main part of the partial differential equation, hyperbolic systems of conservation laws plays an important part in the applications of fluid mechanics,gas dynamics,aerospace,combustion theory,nonlinear elasticity theory and so on. This article considers the generalized Riemann problem for a class of hyperbolic conservation laws ,and summarizes the main results of the existence of its solutions. First we introduce the background of generalized Riemann problem for hyperbolic conservation laws, the development process as well as the present situation; Then we will elaborate on some existence theorems of its global solutions in several kind of situations; Afterward we introduce the use of mathematical methods of studying the generalized Riemann problem for hyperbolic conservation laws; Finally we further discusse several issues of the problem waiting to solve.