Normal deviations from the averaged motion for some reaction–diffusion equations with fast oscillating perturbation
✍ Scribed by Sandra Cerrai
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 347 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0021-7824
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✦ Synopsis
We study the normalized difference between the solution u 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 ū 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 (u -ū)/ √ converges weakly in C([0, T ]; L 2 (0, L)) to the solution of the linearized equation, where an extra Gaussian term appears. Such a term is explicitly given.