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Upper semicontinuity of attractors for small random perturbations of dynamical systems. (English) Zbl 0917.35169
The authors study the relationship between a random attractor and the deterministic one, when they apply to the deterministic partial differential equation a small random perturbation, whose strength is measured by a small parameter $\varepsilon$. Under some conditions, they prove that the random attractor is a perturbation of the deterministic one, in the sense that the upper-semicontinuity for random attractors is obtained as $\varepsilon$ goes to zero. The results are applied to Navier-Stokes equations and to a problem of reaction-diffusion type, both perturbed by an additive white noise.

35R60PDEs with randomness, stochastic PDE
60H15Stochastic partial differential equations
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