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New Structures of Non-selfsimilar Solutions for Multi-dimensional Conservation Laws

Author: WeiTao
Tutor: YangXiaoZhou
School: Shantou University
Course: Applied Mathematics
Keywords: Conservation law elementary wave shock wave rarefaction wave envelope
CLC: O175
Type: Master's thesis
Year: 2007
Downloads: 37
Quote: 0
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Abstract


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.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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