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  $\beta\in(1,\infty)$.

Anexos:

• tertu.pdf