On non-existence of global solutions to a class of stochastic heat equations

Abstract

We consider nonlinear parabolic SPDEs of the form ! tu = ! (! ! )! /2u + b(u )+ (u )˙ w ,w here ˙ w denotes space-time white noise. The functions b and are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.