Stochastic Porous Media Equations
Stochastic Porous Media Equations
Springer | Mathematics | November 2016 | ISBN-10: 3319410687 | 202 pages | pdf | 2.17 mb
Springer | Mathematics | November 2016 | ISBN-10: 3319410687 | 202 pages | pdf | 2.17 mb
Authors: Barbu, Viorel, Da Prato, Giuseppe, Röckner, Michael
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
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.
Number of Pages
IX, 202
Topics
Probability Theory and Stochastic Processes
Partial Differential Equations
Fluid- and Aerodynamics
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