Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations: Stochastic Manifolds for Nonlinear SPDEs II

di Mickaël D. Chekroun (Autore)

Honghu Liu (Autore)

Shouhong Wang (Autore)

Springer International Publishing AG, 2015

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.

• Autore: Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
• Editore: Springer International Publishing AG
• Collana: SpringerBriefs in Mathematics
• Anno: 2015
• Rilegatura: Paperback / softback
• Pagine: 129 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783319125190

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