THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS∗

doi:10.1007/s10473-023-0416-9

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1717-1734.doi: 10.1007/s10473-023-0416-9

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗

Fen HE¹, Zhen WANG^1,†, Tingting CHEN²

1. Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China;
2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

收稿日期:2022-01-05 修回日期:2022-06-07 发布日期:2023-08-08
通讯作者: †Zhen WANG, E-mail: zwang@whut.edu.cn
作者简介:Fen HE, E-mail: fenhe.zky@foxmail.com;Tingting CHEN, E-mail: chenting0617@163.com
基金资助:
*National Natural Science Foundation of China (11771442).

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗

Fen HE¹, Zhen WANG^1,†, Tingting CHEN²

1. Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China;
2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received:2022-01-05 Revised:2022-06-07 Published:2023-08-08
Contact: †Zhen WANG, E-mail: zwang@whut.edu.cn
About author:Fen HE, E-mail: fenhe.zky@foxmail.com;Tingting CHEN, E-mail: chenting0617@163.com
Supported by:
*National Natural Science Foundation of China (11771442).

摘要/Abstract

摘要： In this paper, we study the shock waves for a mixed-type system from chemotaxis. We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region. Under the generalized entropy conditions, we find that there are different shock wave structures for different parameters. To guarantee the uniqueness of the solutions, we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters. Finally, we construct the Riemann solutions in some solvable regions.

关键词: mixed-type, shock waves, entropy condition, chemotaxis, conservation laws

Abstract: In this paper, we study the shock waves for a mixed-type system from chemotaxis. We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region. Under the generalized entropy conditions, we find that there are different shock wave structures for different parameters. To guarantee the uniqueness of the solutions, we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters. Finally, we construct the Riemann solutions in some solvable regions.

Key words: mixed-type, shock waves, entropy condition, chemotaxis, conservation laws

Fen HE, Zhen WANG, Tingting CHEN. THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1717-1734.

Fen HE, Zhen WANG, Tingting CHEN. THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1717-1734.

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THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS^∗

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