Random attractors for singular stochastic partial differential equations
- Authors: Benjamin Gess
- Preprint year: 2011
- First public date: 2011-11-01
- arXiv: 1111.0205
- Status: Published
- Publication type: Journal article
- Publication year: 2013
- Journal: Journal of differential equations, 255 (2013) 3, pp. 524-559
- DOI: 10.1016/j.jde.2013.04.023
Abstract
The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational approach to SPDE with compact embeddings in the Gelfand triple and singular coercivity. For ergodic, monotone, contractive random dynamical systems it is proven that the attractor consists of a single random point. In case of real, linear multiplicative noise finite time extinction is obtained. Applications include stochastic generalized fast diffusion equations and stochastic generalized singular p-Laplace equations perturbed by Levy noise with jump measure having finite first and second moments.