Decay bounds for solutions of second order parabolic problems and their derivatives IV

Abstract

This article continues the derivation of explicit solution and gradient bounds for classes of second order nonlinear parabolic initial-boundary value problems. Earlier results were restricted to domains with boundaries of nonnegative average curvature. The purpose of the present article is to remove the curvature restriction and to extend the results to more general parabolic problems.

Keywords:

• Quasilinear parabolic problems
• Maximum principle
• AMS Classifications: 35K55
• 35K60
• 35K20