`a`

Bounds for blow-up time in nonlinear parabolic systems

Pages: 1025 - 1031, Issue Special, September 2011

 Abstract        Full Text (305.9K)              

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: We consider a nonlinear parabolic system with Neumann boundary conditions which solution may blow up in nite time $t*$ We determine a lower bound for $t*$ by using a Sobolev type inequality. In addition an upper bound for $t*$ is obtained, under alternative conditions on the non linearities.

Keywords:  parabolic systems, blow-up solutions
Mathematics Subject Classification:  Primary: 35K50, 35K60; Secondary: 35K55

Received: July 2010;      Revised: February 2011;      Published: October 2011.