On  global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients

Monica Marras; Stella Vernier Piro

doi:10.3934/proc.2013.2013.535

Article Contents

2013, Volume 2013: 535-544. Doi: 10.3934/proc.2013.2013.535 open access

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On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients

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

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

Received: August 31, 2012

Revised: November 30, 2012

Published: October 2013

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Abstract

This paper deals with the blow-up of the solutions to a class of nonlinear parabolic equations with Dirichlet boundary condition and time dependent coefficients. Under some conditions on the data and geometry of the spatial domain, explicit upper and lower bounds for the blow-up time are derived. Moreover, the influence of the data on the behaviour of the solution is investigated to obtain global existence.

Keywords:

Parabolic problems,
blow-up solutions.

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

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References

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