Approximation of stochastic invariant manifolds stochastic manifolds for nonlinear SPDEs I / [electronic resource] :

• 作者： Chekroun, Mickael D.
• 其他作者：
  • Liu, Honghu.
  • Wang, Shouhong.
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in mathematics,
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in mathematics,
• 主題： Stochastic partial differential equations. , Mathematics , Dynamical Systems and Ergodic Theory. , Partial Differential Equations. , Probability Theory and Stochastic Processes. , Ordinary Differential Equations.
• ISBN： 9783319124964 (electronic bk.) 、 9783319124957 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
• More
• 摘要註: 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.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: