Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1646-1669.

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Global Existence and Convergence of Solutions to a Chemotactic Model with Logarithmic Sensitivity and Mixed Boundary Conditions

Juan Wang(),Zixia Yuan*()   

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731
  • Received:2019-08-30 Online:2020-12-26 Published:2020-12-29
  • Contact: Zixia Yuan;
  • Supported by:
    the Fundamental Research Funds for the Central Universities, UESTC(ZYGX2019J096)


This paper investigates the following chemotactic model with logarithmic sensitivity in a one-dimensional bounded domain: By using a Cole-Hopf type transformation, we transform the above singular repulsive chemotaxis model into a non-singular system of the form Then under some mixed boundary conditions, we prove the global existence and exponential convergence of solutions to the initial-boundary value problem of the above system with regular initial data.

Key words: Chemotaxis, Logarithmic sensitivity, Mixed boundary conditions, Global existence, Exponential convergence

CLC Number: 

  • 0175.2