Hydrodynamics for asymmetric simple exclusion on a finite segment with Glauber-type source

Abstract

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a relaxation term. Different from the usual boundary conditions introduced in [Bardos, Roux, and Nedelec, (1979), Comm. Part. Diff. Equ], discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme.

References in corpus (6)

• Steady-state selection in driven diffusive systems with open boundaries
• Exclusion process with slow boundary
• Derivation of the Leroux system as the hydrodynamic limit of a two-component lattice gas
• Current reservoirs in the simple exclusion process
• Quasi-static limit for the asymmetric simple exclusion
• Scalar conservation law in a bounded domain with strong source at boundary