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  • © 2016

Stochastic Porous Media Equations

  • 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

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
  2. Introduction

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 1-18
  3. Equations with Lipschitz Nonlinearities

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 19-47
  4. Equations with Maximal Monotone Nonlinearities

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 49-93
  5. Variational Approach to Stochastic Porous Media Equations

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 95-106
  6. L 1-Based Approach to Existence Theory for Stochastic Porous Media Equations

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 107-131
  7. The Stochastic Porous Media Equations in \(\mathbb{R}^{d}\)

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 133-165
  8. Transition Semigroup

    • Viorel Barbu, Giuseppe Da Prato, Michael Röckner
    Pages 167-195
  9. Back Matter

    Pages 197-204

About this book

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.

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)

Authors and Affiliations

  • Department of Mathematics, Al. I. Cuza University & Octav Mayer Institute of Mathematics of the Romanian Academy, Iasi, Romania

    Viorel Barbu

  • Classe di Scienze, Scuola Normale Superiore di Pisa , Pisa, Italy

    Giuseppe Da Prato

  • Department of Mathematics, University of Bielefeld , Bielefeld, Germany

    Michael Röckner

Bibliographic Information

Buy it now

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
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