Stochastic Porous Media Equations

Authors: Viorel Barbu, Giuseppe Da Prato, Michael Röckner



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".

Table of contents

Front Matter

Introduction

Equations with Lipschitz Nonlinearities

Equations with Maximal Monotone Nonlinearities

Variational Approach to Stochastic Porous Media Equations

L 1-Based Approach to Existence Theory for Stochastic Porous Media Equations

The Stochastic Porous Media Equations in ℝdRd

Transition Semigroup

Back Matter