Preprint C128/2011
Some results on Hydrodynamical Limit of Exclusion Process in Non-homogeneous Medium

Tertuliano Franco

**Keywords: **
Hydrodynamic limit | exclusion process | non-homegeneous medium

We present here three results concerned on hydrodynamical
limit of exclusion process. The first one: for
conductances driven by any increasing function W, the
time evolution of the spatial density of particles is given
by a parabolic partial equation associated to a symmetric
operator (d/dx)(d/dW) , expressing a large class of nonhomogeneous
cases. The second one is about a d-
dimensional case, where slow bonds (bonds of conductance
of order $N^{-1}$) models a membrane slowing down
the passage of particles between two regions. It is also
proved the hydrodynamical limit of such case. At last,
the third result: for the one-dimensional case with finite
slow bonds of parameter $N^{−\beta}$, the hydrodynamical limit
has three different behaviors depending if $\beta\in[0, 1)$,
$\beta = 1$ or $\beta\in(1,\infty)$.