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The effect of noise on the Chafee-Infante equation : a nonlinear case study
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Caraballo, Tomas, Crauel, Hans, Langa, José A. and Robinson, James C. (2006) The effect of noise on the Chafee-Infante equation : a nonlinear case study. Proceedings of the American Mathematical Society, Volume 135 (Number 2). pp. 373-382.
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Official URL: http://www.ams.org/journals/proc/2007-135-02/S0002...
Abstract
We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, u(t) - Delta u = beta u- u(3), by noise. While a single multiplicative Ito 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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
| Publisher: | American Mathematical Society | ||||
| ISSN: | 0002-9939 | ||||
| Official Date: | 2006 | ||||
| Dates: |
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| Volume: | Volume 135 | ||||
| Number: | Number 2 | ||||
| Number of Pages: | 10 | ||||
| Page Range: | pp. 373-382 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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