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arxiv: 0801.2478 · v1 · pith:GUT7ZFGKnew · submitted 2008-01-16 · 🧮 math.PR · math-ph· math.AP· math.MP

Stochastic Porous Media Equation and Self-Organized Criticality

Viorel Barbu (Institute of Mathematics "Octav Mayer" , Iasi , Romania) , Giuseppe Da Prato (Scuola Normale Superiore di Pisa , Italy) , Michael R\"ockner (Faculty of Mathematics , Bielefeld , Germany
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Departments of Mathematics Statistics Purdue University USA)
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classification 🧮 math.PR math-phmath.APmath.MP
keywords stochasticcriticalequationsmediaporousprovenself-organizedsolutions
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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.

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