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Random attractors for stochastic reaction-diffusion equations on unbounded domains. (English) Zbl 1155.35112
Summary: The existence of a pullback attractor is established for a stochastic reaction-diffusion equation on all \(n\)-dimensional space. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise. The reaction-diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far-field values of solutions.

MSC:
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
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