Lecture Notes in Mathematics: École d’Été de Probabilités de Saint-Flour XL – 2010

Flandoli, Franco

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.

Details

Published by: Springer

Publication Date: 2011-03-11

Format: Paperback

ISBN-13: 9783642182303

DOI: 10.1007/978-3-642-18231-0

Dimensions: 235cm x155cm

Pages: 182