非齐次二维Burgers方程的非自相似黎曼解的奇性结构

Abstract

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

CLC Number:

O175

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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References 17

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

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