Non–existence of global solutions to anisotropic Fujita–type systems of semilinear parabolic equations

Abstract

Two different techniques with which to construct subsolutions to anisotropic Fujita–type systems of semilinear parabolic equations on bounded or unbounded domains are developed. The first makes use of the principal eigenfunction of an associated boundary–value problem (bounded domains) or the fundamental solution of the ‘backward’ heat equation (unbounded domains) to cast the problem into a set of integral inequalities. The second is a generalization of a technique developed by Weissler. A series of theorems concerning global non–existence of solutions is established by applying these techniques.