Stochastic Porous Media Equation and Self-Organized Criticality

Abstract

The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states.

29 pages, BiBoS-Preprint No. 07-11-268

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