New Structures Of Non-selfsimilar Solutions For Multi-dimensional Conservation Laws

In this paper, we get non-selfsimilar elementary waves of the conserva-tion laws in another kind of view, which is different from the usual self-similartransformation. The solution has different global structure at any fixed time t.This paper is divided into three parts.The first part of the paper is introduction. In the second part, we dis-cuss non-selfsimilar elementary waves and their interactions of a class of two-dimensional conservation laws. In this case, we consider the case that the initialdiscontinuity is parabola with u_+＞0, while explicit non-selfsimilar rarefactionwave can be obtained. In the third part, we consider the solution structure ofcase u_+＜0.The new solution structures are obtained by the interactions between dif-ferent elementary waves, and will continue to interact with other states. Globalsolutions will be very different from the situation of one dimension.