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

Two different techniques with which to construct subsolutions to anisotropi c Fujita-type systems of semilinear parabolic equations on bounded or unbou nded domains are developed. The first makes use of the principal eigenfunct ion of an associated boundary-value problem (bounded domains) or the fundam ental solution of the 'backward' heat equation (unbounded domains) to cast the problem into a set of integral inequalities. The second is a generaliza tion of a technique developed by Weissler. A series of theorems concerning global non-existence of solutions is established by applying these techniqu es.