The effect of noise on the chafee-infante equation : A nonlinear case study
The effect of noise on the chafee-infante equation : A nonlinear case study
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DOI：
10.1090/s0002-9939-06-08593-5
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
T. Caraballo;H. Crauel;J. Langa;James C. Robinson
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文献类型：
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作者：
T. Caraballo;H. Crauel;J. Langa;James C. Robinson
我们研究了噪声扰动 Chafee-Infante 标量反应扩散方程 u(t) - Delta u = beta u- u(3) 的影响。虽然足够强度的单个乘法伊藤噪声将稳定原点，但其对应的斯特拉托诺维奇噪声使吸引子的尺寸基本上保持不变。然后我们证明，乘性斯特拉托诺维奇项的集合可以使原点呈指数稳定，而足够丰富的加性噪声将随机吸引子减少到单个点。
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.