American Institute of Mathematical Sciences

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2007, 2007(Special): 704-712. doi: 10.3934/proc.2007.2007.704

Blow up and decay bounds in guasi linear parabolic problems

Monica Marras 1, and  Stella Vernier Piro 1,

1. 

Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy, Italy

Received  September 2006 Revised  May 2007 Published  September 2007

Aim of this paper is to investigate a class of quasilinear parabolic problems whose solutions may blow up at some finite time. We establish conditions on data sufficient to preclude blow up and to insure that the solution and its spatial gradient decay exponentially for all $t > 0$.
Keywords: maximum principles, decay estimates., Nonlinear parabolic problems.
Mathematics Subject Classification: Primary: 35K55, 35B50; Secondary: 35K2.
Citation: Monica Marras, Stella Vernier Piro. Blow up and decay bounds in guasi linear parabolic problems. Conference Publications, 2007, 2007 (Special) : 704-712. doi: 10.3934/proc.2007.2007.704
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