Singular Structure Of The Non-selfsimilar Global Solution For A Class Of Two-dimensional Conservation Law

For the non-selfsimilar Riemann problem of the two-dimensional non-homogeneous conser-vation law, by using the method which is different from the usual self-similar transformation, we can get the two-dimensional non-homogeneous basic waves and the global solution which can be obtained after they interact with each other, and obtain that the global solution has the special structure at any time.This paper is mainly divided into the following three parts:The first part is introduction of the basic background. The second part, we discuss the basic waves of one kind of two-dimensional conservation law and the interaction of them; In this part, we solve the case of initial discontinuity curve is the parabolic curve, for the case of u+> 0, we first solve and get the structures of non-selfsimilar shock wave and non-selfsimilar rarefaction wave which emit from the different parts of its initial discontinuity curve and the structures of interaction with each other; at the same time, with the developing of time, the non-selfsimilar shock wave and the non-selfsimilar rarefaction wave will interact with each other continuously. By studying the interaction of big time, we construct the global solution of this situation. The third part, we discuss the non-selfsimilar shock wave and the non-selfsimilar rarefaction wave which emit from the initial discontinuity when u+<0, study the interaction with each other and the decay of large time, then obtain the structure of its global solution.We find that the global solution of non-selfsimilar Riemann problem of the two-dimensional conservation law is very different from the one dimensional conservation law.