We study the normalized difference between the solution uε of a reaction-diffusion equation in a bounded interval [0, L], perturbed by a fast oscillating term arising as the solution of a stochastic reaction-diffusion equation with a strong mixing behavior, and the solution u ̄ of the corresponding averaged equation. We assume the smoothness of the reaction coefficient and we prove that a central limit type theorem holds. Namely, we show that the normalized difference (uε −u ̄)/√ε converges weakly in C([0, T ]; L2(0, L)) to the solution of the linearized equation, where an extra Gaussian term appears. Such a term is explicitly given.
Normal deviations from the averaged motion for some reaction-diffusion equation with fast oscil lating perturbation / S.CERRAI. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 91:(2009), pp. 614-647.
Normal deviations from the averaged motion for some reaction-diffusion equation with fast oscil lating perturbation
CERRAI, SANDRA
2009
Abstract
We study the normalized difference between the solution uε of a reaction-diffusion equation in a bounded interval [0, L], perturbed by a fast oscillating term arising as the solution of a stochastic reaction-diffusion equation with a strong mixing behavior, and the solution u ̄ of the corresponding averaged equation. We assume the smoothness of the reaction coefficient and we prove that a central limit type theorem holds. Namely, we show that the normalized difference (uε −u ̄)/√ε converges weakly in C([0, T ]; L2(0, L)) to the solution of the linearized equation, where an extra Gaussian term appears. Such a term is explicitly given.File | Dimensione | Formato | |
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