Authors:
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)
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsThis is a preview of subscription content, access via your institution.
Table of contents (7 chapters)
-
Front Matter
-
Back Matter
About this book
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
- partial differential equations
- fluid- and aerodynamics
Reviews
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
Book Title: Stochastic Porous Media Equations
Authors: Viorel Barbu, Giuseppe Da Prato, Michael Röckner
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-41069-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-41068-5Published: 01 October 2016
eBook ISBN: 978-3-319-41069-2Published: 30 September 2016
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 202
Topics: Probability Theory, Differential Equations, Continuum Mechanics