Decay Bounds for Solutions of Second Order Parabolic Problems and their Derivatives III

Abstract

Further extending investigations carried out in previous papers, the authors deal in this paper with another non-linear initial-boundary value problem whose solution, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to determine conditions on the geometry and data sufficient to insure that the solution remains bounded and with those conditions to derive exponential decay bounds for the solution and its gradient.