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arXiv 0802.0633math.APmath.PR
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Time--space white noise eliminates global solutions in reaction diffusion equations

Julián Fernández Bonder, Pablo Groisman

英文摘要:

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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