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The effect of noise on the chafee-infante equation: a nonlinear case study

 

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Author: Caraballo Garrido, Tomás
Crauel, Hans
Langa Rosado, José Antonio
Robinson, James C.
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2006
Published in: Proceedings of the American Mathematical Society, 135(2), 373–382
Document type: Article
Abstract: We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. While a single multiplicative Itˆo noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially unchanged. We then show that a collection of multiplicative Stratonovich terms can make the origin exponentially stable, while an additive noise of sufficient richness reduces the random attractor to a single point.
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URI: http://hdl.handle.net/11441/22772

DOI: 10.2307/20534585

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