Stochastic parameterizing manifolds and non-markovian reduced equations [electronic resource] : stochastic manifolds for nonlinear SPDEs II / Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.

Unlimited

Authorized users

Can lend chapters, not whole ebooks

Stochastic parameterizing manifolds and non-markovian reduced equations [electronic resource] : stochastic manifolds for nonlinear SPDEs II / Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.

9783319125206 electronic book
3319125206 electronic book
9783319125190

Cham : Springer, 2015.

English

1 online resource (xvii, 129 pages) : illustrations (some color).

10.1007/978-3-319-12520-6 doi

QA274.25

515/.353

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.

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed January 12, 2015).

SpringerBriefs in mathematics.

Print version: 9783319125190

Online Resources > Ebooks
All Resources