Titre :

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

Auteur(s) :

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

Titre de la revue :

ALEA : Latin American Journal of Probability and Mathematical Statistics

Pagination :

791--823

Éditeur :

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

Date de publication :

2020

ISSN :

1980-0436

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL