SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES

doi:10.1016/S0252-9602(17)30127-3

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 203-219.doi: 10.1016/S0252-9602(17)30127-3

SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES

牛海萍, 王术

College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

收稿日期:2016-12-07 修回日期:2017-10-27 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Haiping NIU,E-mail:niuhaiping@emails.bjut.edu.cn;Shu WANG,E-mail:wangshu@bjut.edu.cn
基金资助:
The second author is supported by the National Natural Science Foundation of China (11371042, 1471028, 11601021) and the Beijing Natural Science Foundation (1142001).

SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES

Haiping NIU, Shu WANG

College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Received:2016-12-07 Revised:2017-10-27 Online:2018-02-25 Published:2018-02-25
Supported by:
The second author is supported by the National Natural Science Foundation of China (11371042, 1471028, 11601021) and the Beijing Natural Science Foundation (1142001).

摘要/Abstract

摘要：

We study the singular structure of a family of two dimensional non-self-similar global solutions and their interactions for quasilinear hyperbolic conservation laws. For the case when the initial discontinuity happens only on two disjoint unit circles and the initial data are two different constant states, global solutions are constructed and some new phenomena are discovered. In the analysis, we first construct the solution for 0 ≤ t < T^*.Then, when T^* ≤ t < T', we get a new shock wave between two rarefactions, and then, when t > T', another shock wave between two shock waves occurs. Finally, we give the large time behavior of the solution when t → ∞. The technique does not involve dimensional reduction or coordinate transformation.

关键词: singular structure, quasilinear hyperbolic equations, elementary wave, global solutions

Abstract:

Key words: singular structure, quasilinear hyperbolic equations, elementary wave, global solutions

牛海萍, 王术. SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES[J]. 数学物理学报(英文版), 2018, 38(1): 203-219.

Haiping NIU, Shu WANG. SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES[J]. Acta mathematica scientia,Series B, 2018, 38(1): 203-219.

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SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES

SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES

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