Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. (English) Zbl 1317.60081
Summary: In this paper, we consider the long term behavior of solutions to stochastic delay parabolic equations with additive noise and deterministic nonautonomous forcing. We first establish the existence of a continuous nonautonomous random dynamical system for the equations. Then we prove pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractors. Finally, we establish the upper semicontinuity of the random attractors when noise intensity and time delay approach zero, respectively.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35B41 | Attractors |
Keywords:
stochastic delay parabolic equations; random attractors; asymptotical compactness; upper semicontinuityReferences:
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