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.
General
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