A free boundary problem for a class of parabolic-elliptic type chemotaxis model

Hua Chen; Wenbin Lv; Shaohua Wu

doi:10.3934/cpaa.2018122

Article Contents

2018, Volume 17, Issue 6: 2577-2592. Doi: 10.3934/cpaa.2018122

This issue Previous Article Regularity of radial stable solutions to semilinear elliptic equations for the fractional Laplacian Next Article The Stochastic 3D globally modified Navier-Stokes equations: Existence, uniqueness and asymptotic behavior

A free boundary problem for a class of parabolic-elliptic type chemotaxis model

1.
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
2.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

* Corresponding author
* Corresponding author

Received: January 31, 2018

Revised: February 28, 2018

Published: June 2018

This work is supported by National Natural Science Foundation of China (Grant No. 11131005) and the Fundamental Research Funds for the Central Universities (Grant No. 2014201020202).

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Abstract

In this paper, we study a free boundary problem for a class of parabolic-elliptic type chemotaxis model in high dimensional symmetry domain Ω. By using the contraction mapping principle and operator semigroup approach, we establish the existence of the solution for such kind of chemotaxis system in the domain Ω with free boundary condition. Besides, we get the explicit formula for the free boundary and show the chemotactic collapse for the solution of the system.

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Mathematics Subject Classification: Primary: 35A01, 35K57, 35R35; Secondary: 47D03.

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