非齐次二维Burgers方程的非自相似黎曼解的奇性结构  

Global Singular Structures of Non-Selfsimilar Riemann Solutions for Two Dimensional Non-homogeneous Burgers Equation

作　　者：赵远安 曹高伟 杨小舟 Zhao Yuan-an;Cao Gaowei;Yang Xiaozhou(University of Chinese Academy of Sciences,Beijing 100049;Innovation Academy for Precision Measurement Science and Technology,Chinese Academy of Sciences,Wuhan 430071)

机构地区：[1]中国科学院大学,北京100049 [2]中国科学院精密测量科学与技术创新研究院,武汉430071

出　　处：《数学物理学报（A辑）》2022年第4期1122-1149,共28页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701551,11971024,11471332)。

摘　　要：该文研究了二维非齐次Burgers方程Riemann问题的激波解和稀疏波解之间相互作用的全局奇性结构及其演化,其中初值被两个相离的圆隔开并分成三片常数.首先得到了由初值间断发出的激波解和稀疏波解的表达式;其次,讨论了这些激波和稀疏波的相互作用,并发现了一些新现象,其与齐次情形相比,激波和稀疏波能一直相互作用,相互作用的时间没有使得结构发生改变的临界值;最后构造了非自相似解的全局结构,并发现了有别于齐次情形的渐近行为,即基本波区域的直径是有界的.We investigate the global structures and wave interactions of non-selfsimilar solutions for two dimensional non-homogeneous Burgers equation,where the initial data has three constant states,separated by two disjoint circles.We first get the expressions of solutions of shock waves and rarefaction waves starting from the initial discontinuity.Secondly,we discuss the interactions of these elementary waves and find some new phenomena that the time of the interaction of shock wave and rarefaction wave has no critical point at which the structures begin to change,which are different from the homogeneous case.Finally,we construct the global structures of the non-selfsimilar solutions and find the new asymptotic behavior that the diameter of the region of elementary waves is bounded.

关 键 词：非齐次Burgers方程 RIEMANN问题 全局奇性结构 非自相似解 

分 类 号：O175[理学—数学]