Non-selfsimilar Elementary Waves Of The Multi-dimensional Scalar Conservation Law And Their Interactions

In this thesis, we get the non-selfsimilar elementary waves for multi-dimensi -onal Scalar conservation equation and their global analytic .solution in another kind of approach, which is different from usual self-similar transformation. The solution has new structure for any fixed time t.This thesis is divided into three parts.In the first part of the thesis, we discuss elementary waves and their interactions for two-dimensional equation. In this case,we let the initial discontinuity divide the initial plane into two infinite parts. We get the global analytic solution specifically where the initial discontinuity is parabola for two-dimensional equation.In the second part of the thesis,we consider another special kind of two-dimensional equation's elementary waves and their interactions. In this case, the initial discontinuity divide the initial plane into an infinite region and a finite closed region. It is explicit that the distribution of the solution in this case is different from the former in essence. We study the case that the initial discontinuity is a unit circle and a concave closed curve separately for two-dimensional equation and we find that the global solution of two-dirnensional Scalar conservation equation can vary freely.In the last part of the thesis.we study elementary waves and their interactions for a three-dimensional equation. Here the distribution is a unit sphere and we get the three-dimensional solution for the three-dimensional equation while we cannot get it in usual self-similar mathod. The result we get is one of the least achievements for non-symmetric type in three-dimensional conservation equation.