IJPAM: Volume 48, No. 2 (2008)

BLOW-UP PHENOMENA FOR
SOME NONLINEAR PARABOLIC SYSTEMS

L.E. Payne$^1$, P.W. Schaefer$^2$
$^1$Department of Mathematics
Cornell University
Ithaca, NY 14853, USA
e-mail: lep8@cornell.edu
$^2$Department of Mathematics
University of Tennessee
1403, Circle Drive, Knoxville, TN 37916, USA
e-mail: schaefer@math.utk.edu


Abstract.A lower bound on the blow-up time for the solution of a system of parabolic equations coupled through their nonlinearities is determined by a first order differential inequality technique. A criterion which ensures that blow-up does not occur and a criterion which ensures that blow-up does occur are also given.

Received: June 19, 2008

AMS Subject Classification: 35K50, 35K60

Key Words and Phrases: parabolic systems, nonlinear problems, blow-up solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2