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Blow up and decay bounds in guasi linear parabolic problems

Pages: 704 - 712, Issue Special, September 2007

 Abstract        Full Text (179.2K)              

Monica Marras - Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy (email)
Stella Vernier Piro - Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy (email)

Abstract: 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:  Nonlinear parabolic problems, maximum principles, decay estimates.
Mathematics Subject Classification:  Primary: 35K55, 35B50; Secondary: 35K20.

Received: September 2006;      Revised: May 2007;      Published: September 2007.