Hydrodynamics for One-Dimensional ASEP in Contact with a Class of Reservoirs
Xu, Lu (2022), Hydrodynamics for One-Dimensional ASEP in Contact with a Class of Reservoirs, Journal of Statistical Physics, 189, 1. 10.1007/s10955-022-02963-x
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Article accepté pour publication ou publiéDate
2022Journal name
Journal of Statistical PhysicsVolume
189Number
1Publisher
Springer
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We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size n. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We investigate two types of reservoirs: (1) the reservoirs that are weakened by nθ for some θ<0 and (2) the reservoirs that create particles only at the right boundary and annihilate particles only at the left boundary. We prove that the spatial density of particles, under the hyperbolic time scale, evolves with the entropy solution to a scalar conservation law on [0, 1] with boundary conditions. The boundary conditions are characterised by the boundary traces [3, 17, 20] at x=0 and x=1 which take values from {0,1}.Subjects / Keywords
Asymmetric simple exclusion process; Slow boundary; Hydrodynamic limit; Entropy solution; Boundary traceRelated items
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