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

Abstract

We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega \subset {\mathbb{R}}^N$, $N\ge 2$. 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.