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Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries
Lu Xu · 2021-08-21 · via math.PR updates on arXiv.org

We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\ldots,N\}$. 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 $N^θ$ with $θ>0$. 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.

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