Journal of Jilin University Science Edition

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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. 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

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

CLC Number: 

  • O175.29