# American Institute of Mathematical Sciences

February  2016, 36(2): 805-832. doi: 10.3934/dcds.2016.36.805

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

 1 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China 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, China 5 School of Mathematical Sciences, Shanxi University, Taiyuan, 030006

Received  June 2014 Revised  July 2014 Published  August 2015

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.
Citation: Xin Lai, Xinfu Chen, Mingxin Wang, Cong Qin, Yajing Zhang. Existence, uniqueness, and stability of bubble solutions of a chemotaxis model. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 805-832. doi: 10.3934/dcds.2016.36.805
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