| Dewey Class |
515.353 |
| Title |
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations ([EBook]) : Stochastic Manifolds for Nonlinear SPDEs II / / by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang. |
| Author |
Chekroun, Mickaël D. |
| Added Personal Name |
Liu, Honghu author. |
| Wang, Shouhong author. |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2015. |
| Physical Details |
XVII, 129 p. 12 illus., 11 illus. in color. : online resource. |
| Series |
SpringerBriefs in Mathematics 2191-8198 |
| ISBN |
9783319125206 |
| Summary Note |
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.: |
| Contents note |
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. . |
| 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/10.1007/978-3-319-12520-6 |
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