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.
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4058 - 4090
DOI: 10.1137/151003726
ISSN (online): 1095-7154
Copyright
© 2015, Society for Industrial and Applied Mathematics.
History
Submitted: 13 January 2015
Accepted: 3 September 2015
Published online: 29 October 2015
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