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 D⊂Rd, there exist positive solutions whose mean Lp-norm will blow up in finite time for p⩾1, while, if D=Rd, the previous result holds in any compact subset of Rd. Two examples are given to illustrate some application of the theorems.