Differential and Integral Equations

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

G. Viglialoro

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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.

Article information

Source
Differential Integral Equations Volume 29, Number 3/4 (2016), 359-376.

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1455806028

Mathematical Reviews number (MathSciNet)
MR3466170

Zentralblatt MATH identifier
06562180

Subjects
Primary: 35K55: Nonlinear parabolic equations 35B44: Blow-up 92C17: Cell movement (chemotaxis, etc.) 82C22: Interacting particle systems [See also 60K35]

Citation

Viglialoro, G. Blow-up time of a Keller-Segel-type system with Neumann and Robin boundary conditions. Differential Integral Equations 29 (2016), no. 3/4, 359--376. https://projecteuclid.org/euclid.die/1455806028.


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