Article
The effect of noise on the chafee-infante equation: a nonlinear case study
Author/s | Caraballo Garrido, Tomás
![]() ![]() ![]() ![]() ![]() ![]() ![]() Crauel, Hans Langa Rosado, José Antonio ![]() ![]() ![]() ![]() ![]() ![]() ![]() Robinson, James C. |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2006 |
Deposit Date | 2015-02-26 |
Published in |
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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 ... 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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