Description: Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II, Paperback by Chekroun, Mickaël D.; Liu, Honghu; Wang, Shouhong, ISBN 3319125192, ISBN-13 9783319125190, Brand New, Free shipping in the US 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 solutionwhen 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.
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Book Title: Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equ
Number of Pages: Xvii, 129 Pages
Publication Name: Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear Spdes II
Language: English
Publisher: Springer International Publishing A&G
Publication Year: 2015
Subject: Differential Equations / General, Geometry / Differential, System Theory, Mathematical Analysis
Type: Textbook
Item Weight: 16 Oz
Subject Area: Mathematics, Science
Item Length: 9.3 in
Author: Shouhong Wang, Mickaël D. Chekroun, Honghu Liu
Item Width: 6.1 in
Series: Springerbriefs in Mathematics Ser.
Format: Trade Paperback
