Existence, uniqueness, and stability of bubble solutions of a chemotaxis model

Xin  Lai; Xinfu Chen; Mingxin Wang; Cong  Qin; Yajing Zhang

doi:10.3934/dcds.2016.36.805

Article Contents

2016, Volume 36, Issue 2: 805-832. Doi: 10.3934/dcds.2016.36.805

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Existence, uniqueness, and stability of bubble solutions of a chemotaxis model

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
3.
Natural Science Research Center, Harbin Institute of Technology, Harbin 150080
4.
Center for Financial Engineering, Soochow University, Suzhou, 215006
5.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006

Received: June 2014

Revised: July 2014

Published: May 2017

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Abstract

Existence, uniqueness, and stability of Heaviside function like solutions of a Keller and Segel's minimal chemotaxis model are established when a chemotaxis parameter is large enough. Asymptotic expansions of the solution in terms of the large chemotaxis parameter are also derived.

Keywords:

Mathematics Subject Classification: 92C17, 35B30, 35B35, 35G50, 35P20.

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References

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