Blow-up phenomena in reaction-diffusion systems

Monica Marras; Stella Vernier Piro

doi:10.3934/dcds.2012.32.4001

Article Contents

2012, Volume 32, Issue 11: 4001-4014. Doi: 10.3934/dcds.2012.32.4001

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Blow-up phenomena in reaction-diffusion systems

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

1.
Dipartimento di Matematica e Informatica, Università di Cagliari, 09123

Received: November 30, 2010

Revised: August 31, 2011

Published: October 2012

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Abstract

In this paper we deal with the blow-up phenomena of solutions to two different classes of reaction-diffusion systems coupled through nonlinearities with nonlinear boundary conditions. By using a differential inequality technique, we derive upper and lower bounds for the blow-up time, if blow-up occurs. Moreover by introducing suitable auxiliary functions, we give sufficient conditions on data in order to obtain global existence.

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Mathematics Subject Classification: Primary: 35K55, 35K60; Secondary: 35K40.

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