1.

Record Nr.

UNINA9910299781803321

Autore

Chekroun Mickaël D.

Titolo

Stochastic parameterizing manifolds and non-Markovian reduced equations : Stochastic manifolds for nonlinear SPDEs II / / by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015

ISBN

3-319-12520-6

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (141 p.)

Collana

SpringerBriefs in Mathematics, , 2191-8198

Disciplina

519.22

Soggetti

Differential equations, Partial

Dynamics

Ergodic theory

Probabilities

Differential equations

Partial Differential Equations

Dynamical Systems and Ergodic Theory

Probability Theory and Stochastic Processes

Ordinary Differential Equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.