Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (5): 1285-1304.doi: S0252-9602(16)30069-8

• Articles • Previous Articles     Next Articles

SOLVABILITY OF A PARABOLIC-HYPERBOLIC TYPE CHEMOTAXIS SYSTEM IN 1-DIMENSIONAL DOMAIN

Hua CHEN, Wenbin LÜ, Shaohua WU   

  1. School of Mathematics and Statistics;Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China
  • Received:2015-06-25 Revised:2015-10-12 Online:2016-10-25 Published:2016-10-25
  • Supported by:

    Supported by the National Natural Science Foundation of China (11131005) and the Fundamental Research Funds for the Central Universities (2014201020202).

Abstract:

In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.

Key words: parabolic-hyperbolic system, free boundary, chemotaxis model, local existence

CLC Number: 

  • 35A01
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