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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations = Stochastic Manifolds for Nonlinear SPDEs II /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations/ by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.
Reminder of title:	Stochastic Manifolds for Nonlinear SPDEs II /
Author:	Chekroun, Mickaël D.
other author:	Liu, Honghu.
Description:	XVII, 129 p. 12 illus., 11 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-12520-6
ISBN:	9783319125206

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations = Stochastic Manifolds for Nonlinear SPDEs II /
Chekroun, Mickaël D.

Stochastic Parameterizing Manifolds and Non-Markovian Reduced EquationsStochastic Manifolds for Nonlinear SPDEs II /[electronic resource] :by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang. - 1st ed. 2015. - XVII, 129 p. 12 illus., 11 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

General Introduction -- Preliminaries -- Invariant Manifolds -- Pullback Characterization of Approximating, and Parameterizing Manifolds -- Non-Markovian Stochastic Reduced Equations -- On-Markovian Stochastic Reduced Equations on the Fly -- Proof of Lemma 5.1.-References -- Index.

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

ISBN: 9783319125206

Standard No.: 10.1007/978-3-319-12520-6doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations = Stochastic Manifolds for Nonlinear SPDEs II /
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