The effect of noise on the chafee-infante equation: a nonlinear case study
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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/22772 |
| Acceso en línea: | http://hdl.handle.net/11441/22772 https://doi.org/10.2307/20534585 |
| Access Level: | acceso abierto |
| Palabra clave: | Chafee-Infante equation Stochastic stabilisation Random attractor Random equilibrium One-point attractor Attractor collapse |
| Sumario: | 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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