源于趋化性模型双曲抛物系统激波解的存在性

吉林大学学报(理学版)

源于趋化性模型双曲抛物系统激波解的存在性

祝英杰^1,2, 梁波³, 朱天晓¹，司元举⁴

1. 长春大学理学院, 长春 130022; 2. 吉林大学数学研究所, 长春 130012;3. 大连交通大学理学院, 辽宁大连 116028; 4. 吉林省实验中学, 长春 130022

收稿日期:2012-12-28 出版日期:2013-09-26 发布日期:2013-09-17
通讯作者: 祝英杰 E-mail:yingjiezhu2012@163.com

Existence of Shock Waves to a HyperbolicParabolicSystem Arising from Chemotaxis

ZHU Yingjie^1,2, LIANG Bo³, ZHU Tianxiao¹, SI Yuanju⁴

1. College of Science, Changchun University, Changchun 130022, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China;
3. School of Science, Dalian Jiaotong University, Dalian 116028, Liaoning Province, China;4. Experimental Middle School of Jilin Province, Changchun 130022, China

Received:2012-12-28 Online:2013-09-26 Published:2013-09-17
Contact: ZHU Yingjie E-mail:yingjiezhu2012@163.com

摘要/Abstract

摘要：

利用相平面分析技术和Lyapunov型函数证明了源于趋化性生物模型双曲抛物系统黏性激波解的存在性. 结果表明, 激波的左状态和右状态连接为鞍点鞍点连接.

关键词: 激波, 趋化性, 双曲守恒率, Lax熵条件

Abstract:

We proved the existence of viscous shock waves solutions of a quasilinear hyperbolicparabolic system arising from chemotaxis by means of the phase plane analysis and Lyapunov-type function. The research result reveals that the lefthand and righthand states of a Lax shock correspond to saddle nodes.

Key words: shock wave, chemotaxis, conservation law, Lax entropy condition

中图分类号:

O175.29

祝英杰, 梁波, 朱天晓，司元举. 源于趋化性模型双曲抛物系统激波解的存在性[J]. 吉林大学学报(理学版), 2013, 51(05): 815-818.

ZHU Yingjie, LIANG Bo, ZHU Tianxiao, SI Yuanju. Existence of Shock Waves to a HyperbolicParabolicSystem Arising from Chemotaxis[J]. Journal of Jilin University Science Edition, 2013, 51(05): 815-818.