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

• Autore: Chekroun Mickaël D
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• Edizione: 1st ed. 2015.
• Descrizione fisica: 1 online resource (141 p.)
• Disciplina: 519.22
• Soggetto topico: Partial differential equations; Dynamics; Ergodic theory; Probabilities; Differential equations; Partial Differential Equations; Dynamical Systems and Ergodic Theory; Probability Theory and Stochastic Processes; Ordinary Differential Equations
• Persona (resp. second.): LiuHonghu; WangShouhong
• 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.
• Titolo autorizzato: Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
• ISBN: 3-319-12520-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910299781803321
• Lo trovi qui: Univ. Federico II
• Serie: SpringerBriefs in Mathematics, . 2191-8198