Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (5): 834-845.

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Null Controllability of a Nonlinear Keller-Segel Equation

Zhang Liang, Yang Guopeng   

  1. Department of Mathematics, Wuhan University of Technology, Wuhan 430070
  • Received:2016-11-18 Revised:2017-04-16 Online:2017-10-26 Published:2017-10-26
  • Supported by:
    Supported by the NSFC(61573012) and the Hubei Natural Science Foundation (2014CFB337)

Abstract: In this paper, we study the local controllability for a nonlinear Keller-Segel equation coupled by an elliptic partial differential equation and a parabolic one, in which nonlinearity lies both on its drift-diffusion term and population growth. We prove the local null controllability by Kakutani's fixed point theorem. The method is established on the nonlocal structure of the elliptic-parabolic equation so that it can be treated as a single nonlinear parabolic equation.

Key words: Null controllability, Keller-Segel equation, Observability estimate

CLC Number: 

  • O211.4
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