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These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale.
There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach” and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach”. A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
Hamiltonian and Lagrangian flows on center manifolds Автор: Alexander Mielke Год: 1991 |
Calculus of Variations and Geometric Evolution Problems: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held ... Mathematics / Fondazione C.I.M.E., Firenze) Автор: F. Bethuel, G. Huisken, S. Mueller, K. Steffen, S. Hildebrandt, M. Struwe Год: 1999 |
A Concise Course on Stochastic Partial Differential Equations Автор: Claudia Prévôt Год: 2007 |
Concise Course on Stochastic Partial Differential Equations Автор: Claudia Prévôt Год: 2007 |
A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics) Автор: Claudia Prévôt, Michael Röckner Год: 2007 |
A Concise Course On Stochastic Partial Differential Equations Автор: Claudia Prévôt Год: 2007 |