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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations Stochastic Manifolds for Nonlinear SPDEs II /
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)...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 1st ed. 2015. |
| Colección: | SpringerBriefs in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
| Sumario: | 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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| Descripción Física: | XVII, 129 p. 12 illus., 11 illus. in color. online resource. |
| ISBN: | 9783319125206 |
| ISSN: | 2191-8201 |