Title :

Hydrodynamics for the SSEP with non-reversible slow boundary dynamics: part II, below the critical regime

Author(s) :

Erignoux, Clement [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Gonçalves, P [Auteur]
Nahum, G [Auteur]

Journal title :

ALEA : Latin American Journal of Probability and Mathematical Statistics

Pages :

791--823

Publisher :

Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]

Publication date :

2020

ISSN :

1980-0436

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with reservoirs which inject and remove particles in a finite size windows at the extremities of ...
Show more >The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More precisely, the reservoirs inject/remove particles at/from any point of a window of size K placed at each extremity of the bulk and particles are injected/removed to the first open/occupied position in that window. The reservoirs have slow dynamics, in the sense that they intervene at speed N −θ w.r.t. the bulk dynamics. In the first part of this article, [4], we treated the case θ > 1 for which the entropy method can be adapted. We treat here the case where the boundary dynamics is too fast for the Entropy Method to apply. We prove using duality estimates inspired by [2, 3] that the hydrodynamic limit is given by the heat equation with Dirichlet boundary conditions, where the density at the boundaries is fixed by the parameters of the model.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL