Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps
Résumé
We consider an exclusion process with long jumps in the box Λ N = {1,. .. , N − 1}, for N ≥ 2, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is described by a transition probability p(·) which is symmetric, with infinite support but with finite variance. The reservoirs add or remove particles with rate proportional to κN −θ , where κ > 0 and θ ∈. If θ > 0 (resp. θ < 0) the reservoirs add and remove fast (resp. slowly) particles in the bulk. According to the value of θ we prove that the time evolution of the spatial density of particles is described by some reaction-diffusion equations with various boundary conditions.
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