Singular-degenerate multivalued stochastic fast diffusion equations

Abstract

We consider singular-degenerate, multivalued stochastic fast diffusion equations with multiplicative Lipschitz continuous noise. In particular, this includes the stochastic sign fast diffusion equation arising from the Bak-Tang-Wiesenfeld model for self-organized criticality. A well-posedness framework based on stochastic variational inequalities (SVI) is developed, characterizing solutions to the stochastic sign fast diffusion equation, previously obtained in a limiting sense only. Aside from generalizing the SVI approach to stochastic fast diffusion equations we develop a new proof of well-posedness, applicable to general diffusion coefficients. In case of linear multiplicative noise, we prove the existence of (generalized) strong solutions, which entails higher regularity properties of solutions than previously known.

arXiv comment27 pages

References in corpus (4)

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• Multi-valued, singular stochastic evolution inclusions
• Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions
• Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations