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arXiv · 0802.0633

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

Julián Fernández Bonder·Pablo Groisman
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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.

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Julián Fernández Bonder, Pablo Groisman. 2008-11-10. Time--space white noise eliminates global solutions in reaction diffusion equations. https://doi.org/10.1016/j.physd.2008.09.005

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