非齐次二维Burgers方程的非自相似黎曼解的奇性结构

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1122-1149.

非齐次二维Burgers方程的非自相似黎曼解的奇性结构

赵远安^1,²(),曹高伟^2,*(),杨小舟²()

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

收稿日期:2021-05-27 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 曹高伟 E-mail:824141695@qq.com;gwcao@apm.ac.cn;xzyang@wipm.ac.cn
作者简介:赵远安, E-mail: 824141695@qq.com|杨小舟, E-mail: xzyang@wipm.ac.cn
基金资助:
国家自然科学基金(11701551);国家自然科学基金(11971024);国家自然科学基金(11471332)

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

Yuan-an Zhao^1,²(),Gaowei Cao^2,*(),Xiaozhou Yang²()

¹ University of Chinese Academy of Sciences, Beijing 100049
² Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071

Received:2021-05-27 Online:2022-08-26 Published:2022-08-08
Contact: Gaowei Cao E-mail:824141695@qq.com;gwcao@apm.ac.cn;xzyang@wipm.ac.cn
Supported by:
the NSFC(11701551);the NSFC(11971024);the NSFC(11471332)

摘要/Abstract

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.

关键词: 非齐次Burgers方程, Riemann问题, 全局奇性结构, 非自相似解

Abstract:

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.

Key words: Non-homogeneous Burgers equation, Riemann problem, Global singular structure, Non-selfsimilar solution

中图分类号:

O175

赵远安,曹高伟,杨小舟. 非齐次二维Burgers方程的非自相似黎曼解的奇性结构[J]. 数学物理学报, 2022, 42(4): 1122-1149.

Yuan-an Zhao,Gaowei Cao,Xiaozhou Yang. Global Singular Structures of Non-Selfsimilar Riemann Solutions for Two Dimensional Non-homogeneous Burgers Equation[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1122-1149.

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