Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities

被引:39
作者
Bloemker, D. [1 ]
Hairer, M.
Pavliotis, G. A.
机构
[1] Univ Augsburg, Inst Math, D-8900 Augsburg, Germany
[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London, England
基金
英国工程与自然科学研究理事会;
关键词
D O I
10.1088/0951-7715/20/7/009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we derive rigorously amplitude equations for stochastic partial differential equations with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) gets transmitted to the slow modes and, as a result, the amplitude equation contains both additive and multiplicative noise. As an application we study the case of the one-dimensional Burgers equation forced by additive noise in the orthogonal subspace to its dominant modes. The theory developed in the present paper thus allows us to explain theoretically some recent numerical observations on stabilization with additive noise.
引用
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页码:1721 / 1744
页数:24
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