 94387 Michael Ekhaus, Timo Seppalainen
 Stochastic dynamics macroscopically
governed by the porous medium equation
(122K, AMSTeX)
Dec 4, 94

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We introduce a class of interacting lattice models
on the torus whose special feature is that the macroscopic equation
of the empirical density is a degenerate parabolic equation.
The models come in two versions: One with continuous variables and
one with particles on the sites. In the particle model a degenerate
equation is obtained only if the size of the particle vanishes in the
limit, otherwise the limiting equation is a nondegenerate equation that
also governs the densities of certain exclusion processes with speed
change. We establish basic properties of these models such as
attractiveness and reversibility, and prove the hydrodynamic scaling
limits for the empirical densities. As a special case of the degenerate
equation we get the equation of an ideal gas flowing isothermally
through a porous medium.
 Files:
94387.tex