Time--space white noise eliminates global solutions in reaction diffusion equations

Abstract

We prove that perturbing the reaction--diffusion equation $u_t=u_{xx} + (u_+)^p$ ($p>1$), with time--space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists.Comment: New results included. To be published in Physica