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Viac informácií o knihe Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

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Anotácia knihy

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.

Parametre knihy

Zaradenie knihy Knihy po anglicky Mathematics & science Mathematics Calculus & mathematical analysis

• Celý názov: Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
• Podnázov: Stochastic Manifolds for Nonlinear SPDEs II
• Autor: Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
• Jazyk: Angličtina
• Väzba: Brožovaná
• Počet strán: 129
• EAN: 9783319125190
• ISBN: 3319125192
• ID: 07177374
• Nakladateľ: Springer International Publishing AG
• Hmotnosť: 321 g
• Rozmery: 235 × 155 × 235 mm
• Dátum vydania: 24. December 2014

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