Explosive solutions of stochastic reaction–diffusion equations in mean Lp-norm

The paper is concerned with the problem of non-existence of global solutions for a class of stochastic reaction–diffusion equations of Itô type. Under some sufficient conditions on the initial state, the nonlinear term and the multiplicative noise, it is proven that, in a bounded domain , there exist positive solutions whose mean Lp-norm will blow up in finite time for p 1, while, if , the previous result holds in any compact subset of . Two examples are given to illustrate some application of the theorems.