Modulation Equations: Stochastic Bifurcation in Large Domains

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• 作者：D. Bl?mker ; M. Hairer and G. A. Pavliotis
• 刊名：Communications in Mathematical Physics
• 出版年：2005
• 出版时间：September 2005
• 年：2005
• 卷：258
• 期：2
• 页码：479-512
• 全文大小：350 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916

文摘

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations.