Stochastic parameterizing manifolds and non-markovian reduced equations [Documento electrónico] / Mickaël D. Chekroun, Honghu Liu, Shouhong Wang : stochastic manifolds for nonlinear SPDEs II
Language: eng.Country: US - United States of America.Publication: Cham : Springer International Publishing, 2015Description: XVII, 129 p. 12 il.ISBN: 978-3-319-12520-6.Series: SpringerBriefs in mathematicsSubject - Topical Name: 3647 | 9053 | 6798 | 1072Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT | Não Ficção | QA374.SPR FCT 96564 (Browse shelf(Opens below)) | 1 | Available |
Colocação: Online
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.
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