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Random Perturbation of PDEs and Fluid Dynamic Models: École d’Été de Probabilités de Saint-Flour XL – 2010: Lecture Notes in Mathematics, cartea 2015

Autor Franco Flandoli
en Limba Engleză Paperback – 11 mar 2011
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.
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Specificații

ISBN-13: 9783642182303
ISBN-10: 3642182305
Pagini: 176
Ilustrații: X, 182 p. 10 illus.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.3 kg
Ediția:2011
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seriile Lecture Notes in Mathematics, École d'Été de Probabilités de Saint-Flour

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

1. Introduction to Uniqueness and Blow-up.- 2. Regularization by Additive Noise.- 3. Dyadic Models.- 4. Transport Equation.- 5. Other Models. Uniqueness and Singularities

Textul de pe ultima copertă

This volume 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.

Caracteristici

Sometimes SPDEs perform better than PDEs: the book aims to understand when and why Non traditional research directions in SPDE theory are presented The interaction between noise and uniqueness or singularities is investigated Stochastic fluid dynamic models are treated by special techniques Includes supplementary material: sn.pub/extras