NEW STRUCTURES FOR NON-SELFSIMILAR SOLUTIONS OF MULTI-DIMENSIONAL CONSERVATION LAWS  

作　　者：杨小舟 魏涛 

机构地区：[1]Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, West No.30, Xiao Hong Shan [2]Department of Mathematics, Shantou University

出　　处：《Acta Mathematica Scientia》2009年第5期1182-1202,共21页数学物理学报（B辑英文版）

基　　金：Sponsored by the National Natural Science Foundation of China (10671116,10871199, and 10001023);Hou Yingdong Fellowship (81004), The China Scholarship Council, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Natural Science Foundation of Guangdong (06027210 and 000804);Natural Science Foundation of Guangdong Education Bureau (200030)

摘　　要：In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.

关 键 词：non-selfsimilar shock wave rarefaction wave ENVELOPE multi-dimensional conservation laws 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]