Stochastic Porous Media Equations

Focusing on stochastic porous media equations, this book places an emphasis onexistence theorems, asymptotic behavior and ergodic properties of the associatedtransition semigroup. Stochastic perturbations of the porous media equation havereviously been considered by physicists, but rigorous mathematical existenceresults 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 throughporous media, and also thermal propagation in plasma and plasma radiation.Another important application is to a model of the standard self-organized criticalityprocess, 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.