Abstract
We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular diffusion equations such as the stochastic 1-Laplacian evolution (total variation flow) in all space dimensions and the stochastic singular fast-diffusion equation. In case of additive Wiener noise we prove the existence of a unique weak*-mean ergodic invariant measure.
Original language | English |
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Pages (from-to) | 789-827 |
Number of pages | 39 |
Journal | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES |
Volume | 101 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Ergodic semigroup
- Logarithmic diffusion
- p-Laplacian equation
- Singular stochastic evolution equation