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

J. FERNÁNDEZ BONDER; P. GROISMAN

PHYSICA D - NONLINEAR PHENOMENA

ELSEVIER SCIENCE BV

Año: 2009 p. 209 - 215

0167-2789

We prove that perturbing the reactiondiffusion equation $u_t = u_{xx} + (u_+)^p$ $(p > 1)$, with timespace white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists