Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions

Payne, L.; Philippin, G.

doi:10.1090/S0002-9939-2013-11493-0

Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions
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by L. E. Payne and G. A. Philippin

Proc. Amer. Math. Soc. 141 (2013), 2309-2318

DOI: https://doi.org/10.1090/S0002-9939-2013-11493-0

Published electronically: February 20, 2013

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Abstract:

A class of initial boundary value problems for the semilinear heat equation with time dependent coefficients is considered. Using a first order differential inequality technique, the influence of the data on the behaviour of the solutions (blow-up in finite or infinite time, global existence) is investigated. Lower and upper bounds are derived for the blow-up time when blow-up occurs.

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