Bounds for blow-up time in nonlinear parabolic systems

Monica Marras; Stella Vernier Piro

doi:10.3934/proc.2011.2011.1025

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2011, Volume 2011: 1025-1031. Doi: 10.3934/proc.2011.2011.1025 open access

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Bounds for blow-up time in nonlinear parabolic systems

Monica Marras^1, and
Stella Vernier Piro^1,

1.
Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari

Received: June 30, 2010

Revised: January 31, 2011

Published: August 2017

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Abstract

We consider a nonlinear parabolic system with Neumann boundary conditions which solution may blow up in nite time $t*$ We determine a lower bound for $t*$ by using a Sobolev type inequality. In addition an upper bound for $t*$ is obtained, under alternative conditions on the non linearities.

Keywords:

parabolic systems,
blow-up solutions.

Mathematics Subject Classification: Primary: 35K50, 35K60; Secondary: 35K55.

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