Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations

Duan, Jinqiao; Roberts, A. J.; Wang, W.

doi:10.1142/9789814360920_0003

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“…Other aspects of the averaging principle for slow-fast systems of SPDEs have been studied by several other authors, see e.g. [17], [22], [29], [30] and [40].…”

Section: Introductionmentioning

confidence: 99%

Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case

Cerrai¹,

Lunardi²

2017

SIAM J. Math. Anal.

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We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging principle in terms of the invariant measure of the fast equation is not anymore available. As an alternative, we introduce the time depending evolution family of measures associated with the fast equation. Under the assumption that the coefficients in the fast equation are almost periodic, the evolution family of measures is almost periodic. This allows to identify the appropriate averaged equation and prove the validity of the averaging limit. *

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“…Other aspects of the averaging principle for slow-fast systems of SPDEs have been studied by several other authors, see e.g. [17], [22], [29], [30] and [40].…”

Section: Introductionmentioning

confidence: 99%

Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case

Cerrai¹,

Lunardi²

2017

SIAM J. Math. Anal.

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Large deviation for two-time-scale stochastic burgers equation

Sun

Wang

et al. 2020

Stoch. Dyn.

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A Freidlin–Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion, Probab. Math. Statist. 20 (2000) 39–61].

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Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations

Cited by 2 publications

References 28 publications

Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case

Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case

Large deviation for two-time-scale stochastic burgers equation

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