This paper is concerned with a parabolic-parabolic Keller- Segel-type system in a bounded domain ℧ 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.
Blow-up time of a Keller-Segel-type system with Neumann and Robin boundary conditions
VIGLIALORO, GIUSEPPE
2016
Abstract
This paper is concerned with a parabolic-parabolic Keller- Segel-type system in a bounded domain ℧ 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.
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