IJPAM: Volume 42, No. 2 (2008)

SOME PROPERTIES OF SOLUTIONS OF NONLINEAR
PARABOLIC PROBLEMS WITH NEUMANN CONDITIONS

Monica Marras
$^1$Dipartimento di Matematica e Informatica
Università di Cagliari
Viale Merello 92, Cagliari, 09123, ITALY
e-mail: mmarras@unica


Abstract.We investigate the behavior of the solution of a nonlinear parabolic problem, when Neumann conditions are prescribed on the boundary $\partial \Omega \times [0,T]$, $\Omega$ a bounded $R^N$ domain. We determine conditions on the geometry and data to insure a decay bound for the solution and its gradient.

Received: August 17, 2007

AMS Subject Classification: 35K60, 35B40, 35B50

Key Words and Phrases: nonlinear parabolic equation, decay bounds, maximum principles

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2