Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries

Abstract

We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\dots ,N\}$. The particles can be created/annihilated at the boundaries with given rates. These rates are $L^{\infty }$ functions of time and are independent of the jump rates in the bulk. The boundary dynamics is modified by a factor $N^{\hat{I}}¸$ with $\hat{I}¸>0$. We study the hydrodynamic limit for the particle density profile under the hyperbolic space-time scale. The macroscopic equation is given by (inviscid) Burgers equation with Dirichlet type boundaries that is characterized by the boundary entropy. A grading scheme is developed to control the formulation of boundary layers on the microscopic level.

published version