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© 2016

Stochastic Porous Media Equations

Benefits

  • This is the first book on stochastic porous media equations

  • Concentrates on essential points, including existence, uniqueness, ergodicity and finite time extinction results

  • Presents the state of the art of the subject in a concise, but reasonably self-contained way

  • Includes both the slow and fast diffusion case, but also the critical case, modeling self-organized criticality

Book

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

  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

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Reviews

“The authors of the monograph are renowned experts in the field of SPDEs and the book may be of interest not only to SPDE specialists but also to other researchers in mathematics, physics and biology.” (Bohdan Maslowski, Mathematical Reviews, July, 2018)