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Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Approximation of Stochastic Invariant Manifolds ([EBook]) : Stochastic Manifolds for Nonlinear SPDEs I / / by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.
Author	Chekroun, Mickaël D.
Added Personal Name	Liu, Honghu author.
Added Personal Name	Wang, Shouhong author.
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	XV, 127 p. 1 illus. in color. : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9783319124964
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-12496-4
Links to Related Works	Subject References: Differential Equations . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Mathematics . Ordinary differential equations . Partial differential equations . Probabilities . Probability theory and stochastic processes . Authors: Chekroun, Mickaël D. . Liu, Honghu . Wang, Shouhong . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 515.39 . 515.48 .

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

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