Stochastic Porous Media Equations (Lecture Notes in Mathematics, 2163) by Viorel Barbu (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “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) From the Back Cover 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.

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