Random Perturbation of PDEs and Fluid Dynamic Models

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.

Inhaltsverzeichnis

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

Produktdetails

• Autoren: Franco Flandoli
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 01.01.2011
• EAN: 9783642182303
• ISBN: 978-3-642-18230-3
• Seiten: 182
• Abmessung: 155 mm x 236 mm x 13 mm
• Gewicht: 311 g
• Illustration: X, 182 p. 10 illus.
• Serien: Lecture Notes in Mathematics; École d'Été de Probabilités de Saint-Flour
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Stochastik, B, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory