Approximation of Stochastic Invariant Manifolds Stochastic Manifolds for Nonlinear SPDEs I /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Chekroun, Mickaël D. (Autor), Liu, Honghu (Autor), Wang, Shouhong (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:SpringerBriefs in Mathematics,
Temas:
Dynamical systems.
Differential equations.
Probabilities.
Dynamical Systems.
Differential Equations.
Probability Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • General Introduction
  • Stochastic Invariant Manifolds: Background and Main Contributions
  • Preliminaries
  • Stochastic Evolution Equations
  • Random Dynamical Systems
  • Cohomologous Cocycles and Random Evolution Equations
  • Linearized Stochastic Flow and Related Estimates
  • Existence and Attraction Properties of Global Stochastic Invariant Manifolds
  • Existence and Smoothness of Global Stochastic Invariant Manifolds
  • Asymptotic Completeness of Stochastic Invariant Manifolds
  • Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds
  • Local Stochastic Critical Manifolds: Existence and Approximation Formulas
  • Standing Hypotheses
  • Existence of Local Stochastic Critical Manifolds
  • Approximation of Local Stochastic Critical Manifolds
  • Proofs of Theorem 6.1 and Corollary 6.1
  • Approximation of Stochastic Hyperbolic Invariant Manifolds
  • A Classical and Mild Solutions of the Transformed RPDE
  • B Proof of Theorem 4.1
  • References.

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