Global solutions of a Keller--Segel system with saturated logarithmic sensitivity function

Qi Wang

doi:10.3934/cpaa.2015.14.383

Article Contents

2015, Volume 14, Issue 2: 383-396. Doi: 10.3934/cpaa.2015.14.383

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Global solutions of a Keller--Segel system with saturated logarithmic sensitivity function

Qi Wang^1,

1.
Department of Mathematics, Southwestern University of Finance and Economics, 555 Liutai Ave, Wenjiang, Chengdu, Sichuan 611130

Received: October 31, 2013

Revised: August 31, 2014

Published: February 2015

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Abstract

We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided that the ratio of the chemotactic coefficient to the motility of cells is not too large.

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Mathematics Subject Classification: Primary: 92C17, 35B32, 35B35, 35B36, 35B40, 35J47.

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