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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...

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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:
DateEvent
2006Published
Volume: Volume 135
Number: Number 2
Number of Pages: 10
Page Range: pp. 373-382
Status: Peer Reviewed
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

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