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Stochastic Porous Media Equations

  • Viorel Barbu
  • Giuseppe Da Prato
  • Michael Röckner

Part of the Lecture Notes in Mathematics book series (LNM, volume 2163)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 1-18
  3. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 19-47
  4. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 49-93
  5. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 95-106
  6. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 107-131
  7. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 133-165
  8. Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 167-195
  9. Back Matter
    Pages 197-204

About this book

Introduction

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.

The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".

The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Keywords

Primary: 60H15, 35K55, Secondary: 76S99, 76M30, 76M35 Porous Media Equations Gaussian Noise Stochastic Processes Stochastic PDEs Self organizing criticality

Authors and affiliations

  • Viorel Barbu
    • 1
  • Giuseppe Da Prato
    • 2
  • Michael Röckner
    • 3
  1. 1.Department of MathematicsAl. I. Cuza University & Octav Mayer Institute of Mathematics of the Romanian AcademyIasiRomania
  2. 2.Classe di ScienzeScuola Normale Superiore di Pisa PisaItaly
  3. 3.Department of MathematicsUniversity of Bielefeld BielefeldGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-41069-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-41068-5
  • Online ISBN 978-3-319-41069-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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