Comparison results in a class of reaction-diffusion problems

Abstract

In this paper pointwise bounds for the solutionsu (x, t) of some reaction-diffusion problems are derived. They are of the form $$u(x,t)\mathop \geqq \limits_{( \leqq )} \upsilon (x,t)z(t),$$ wherez (t) is the solution of the associated “kinetic equation” andυ (x, t) is the solution of a pure diffusion problem.