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Approximation of Stochastic Invariant Manifolds

Stochastic Manifolds for Nonlinear SPDEs I

  • Mickaël D. Chekroun
  • Honghu Liu
  • Shouhong Wang

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 1-7
  3. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 9-12
  4. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 13-27
  5. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 29-47
  6. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 49-59
  7. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 61-92
  8. Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
    Pages 93-98
  9. Back Matter
    Pages 99-127

About this book

Introduction

This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations  take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.

Keywords

37L65,37D10,37L25,35B42,37L10,37L55. Leading-Order Taylor Approximations Lyapunov-Perron Integrals Stochastic Invariant Manifolds Stochastic Partial Differential Equations Weak Non-Resonance Conditions

Authors and affiliations

  • Mickaël D. Chekroun
    • 1
  • Honghu Liu
    • 2
  • Shouhong Wang
    • 3
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.University of CaliforniaLos AngelesUSA
  3. 3.Indiana UniversityBloomingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-12496-4
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-12495-7
  • Online ISBN 978-3-319-12496-4
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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