Blow-up time of a Keller-Segel-type system with Neumann and Robin boundary conditions

Abstract

This paper is concerned with a parabolic-parabolic Keller-Segel-type system in a bounded domain $\Omega \subset \mathbb{R}^N$ (with $N=2$ or $N=3$) presenting source and damping terms. We impose Neumann and Robin boundary conditions to each one of the two unknowns of the problem and study the non-negative solutions which blow up in finite time $t^*$. In this way, it is possible to derive explicit lower bounds for $t^*$, under appropriate conditions on the data of the problem.