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  • Book
  • © 2011

Random Perturbation of PDEs and Fluid Dynamic Models

École d’Été de Probabilités de Saint-Flour XL – 2010

Authors:

  1. Franco Flandoli

    1. Department of Applied Mathematics, University of Pisa, Pisa, Italy

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  • 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

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2015)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
    PDF

  2. Introduction to Uniqueness and Blow-Up

    • Franco Flandoli
    Pages 1-16

  3. Regularization by Additive Noise

    • Franco Flandoli
    Pages 17-69

  4. Dyadic Models

    • Franco Flandoli
    Pages 71-99

  5. Transport Equation

    • Franco Flandoli
    Pages 101-131

  6. Other Models: Uniqueness and Singularities

    • Franco Flandoli
    Pages 133-159

  7. Back Matter

    Pages 161-176
    PDF
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About this book

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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Keywords

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Authors and Affiliations

  • Department of Applied Mathematics, University of Pisa, Pisa, Italy

    Franco Flandoli

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Bibliographic Information

  • Book Title: Random Perturbation of PDEs and Fluid Dynamic Models

  • Book Subtitle: École d’Été de Probabilités de Saint-Flour XL – 2010

  • Authors: Franco Flandoli

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-18231-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Softcover ISBN: 978-3-642-18230-3Published: 11 March 2011

  • eBook ISBN: 978-3-642-18231-0Published: 02 March 2011

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 182

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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Buy it now

eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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