Regularity of random attractors for stochastic reaction-diffusion equations on unbounded domains. (English) Zbl 1331.35409
Summary: The existence of a unique random attractors in \(H^1(\mathbb{R}^n)\) for a stochastic reaction-diffusion equation with time-dependent external forces is proved. Due to the presence of both random and non-autonomous deterministic terms, we use a new theory of random attractors which is introduced in [B. Wang, J. Differ. Equations 253, No. 5, 1544–1583 (2012; Zbl 1252.35081)] instead of the usual one. The asymptotic compactness of solutions in \(H^1(\mathbb{R}^n)\) is established by combining “tail estimate” technique and some new estimates on solutions. This work improves some recent results about the regularity of random attractors for stochastic reaction-diffusion equations.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B41 | Attractors |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
Keywords:
random dynamical systems; random attractors; stochastic reaction-diffusion equations; unbounded domains; tail estimatesCitations:
Zbl 1252.35081References:
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