Invariant foliations for stochastic partial differential equations with dynamic boundary conditions

Zhongkai  Guo

doi:10.3934/dcds.2015.35.5203

Article Contents

2015, Volume 35, Issue 11: 5203-5219. Doi: 10.3934/dcds.2015.35.5203

This issue Previous Article The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator Next Article Large deviation principle for stochastic heat equation with memory

Invariant foliations for stochastic partial differential equations with dynamic boundary conditions

Zhongkai Guo^1,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074

Received: August 31, 2013

Revised: February 28, 2014

Published: October 2015

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Abstract

Invariant foliations are geometric structures useful for describing and understanding qualitative behaviors of nonlinear dynamical systems. They decompose the state space into regions of different dynamical regimes, and thus help depict dynamics. We investigate invariant foliations for a class of stochastic partial differential equations with random dynamical boundary conditions, and then provide an approximation for these foliations when the noise intensity is sufficiently small.

Keywords:

Stochastic partial differential equation,
invariant foliations,
dynamic boundary,
analytical approximations.

Mathematics Subject Classification: Primary: 34F05, 34C45; Secondary: 37H10, 60H10.

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