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Random Perturbation of PDEs and Fluid Dynamic Models
Franco Flandoli
其他書名
École d’Été de Probabilités de Saint-Flour XL – 2010
出版Springer, 2011-03-02
主題Mathematics / Probability & Statistics / GeneralMathematics / Probability & Statistics / Stochastic Processes
ISBN36421823139783642182310
URLhttp://books.google.com.hk/books?id=K-L7CAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.