Singular-degenerate multivalued stochastic fast diffusion equations
- Authors: Benjamin Gess, Michael Röckner
- Preprint year: 2015
- First public date: 2015-01-07
- arXiv: 1501.01544
- Status: Published
- Publication type: Journal article
- Publication year: 2015
- Journal: SIAM journal on mathematical analysis, 47 (2015) 5, pp. 4058-4090
- DOI: 10.1137/151003726
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.