POINTWISE BOUNDS AND SPATIAL DECAY ESTIMATES IN HEAT CONDUCTION PROBLEMS
Lawrence Edward Payne, Gérard A. Philippin · Mathematical Models and Methods in Applied Sciences · 1995
In this paper we derive a new maximum principle for the absolute value of the gradient of a solution to the heat equation. We then apply this principle to obtain explicit bounds in the associated Dirichlet problem. Finally we derive explicit pointwise St-Venant type spatial decay estimates for solutions of certain initial-boundary value problems and their gradients in the case of unbounded domains.