Random attractors for stochastic reaction-diffusion equations with multiplicative noise in \(H_0^1\)
The existence of a random \((L^2,H_0^1)\)-pullback set attractor for the random dynamical system (RDS) induced by a stochastic reaction-diffusion equation with a scalar multiplicative Wiener process in the Stratonovich sense is established. This is achieved by proving the existence of sufficiently big absorbing random balls together with the asymptotic compactness of the RDS, both for tempered bounded sets.
scientific article; zbMATH DE number 6368943
scientific article