Blow-up time of a Keller-Segel-type system with Neumann and Robin boundary conditions. (English) Zbl 1374.35217
Summary: 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 \(t^{\ast}\). In this way, it is possible to derive explicit lower bounds for \(t^{\ast}\), under appropriate conditions on the data of the problem.
MSC:
35K55 | Nonlinear parabolic equations |
35B44 | Blow-up in context of PDEs |
92C17 | Cell movement (chemotaxis, etc.) |
82C22 | Interacting particle systems in time-dependent statistical mechanics |