Diffusion limit for a kinetic equation with a thermostatted interface

Basile, Giada; Komorowski, Tomasz; Olla, Stefano

Basile, Giada; Komorowski, Tomasz; Olla, Stefano (2019), Diffusion limit for a kinetic equation with a thermostatted interface, Kinetic & Related Models, 12, 5, p. 1185-1196. 10.3934/krm.2019045

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Type

Article accepté pour publication ou publié

Date

2019

Nom de la revue

Kinetic & Related Models

Volume

Numéro

Éditeur

AIMS - American Institute of Mathematical Sciences

Ville d’édition

Paris

Pages

1185-1196

Identifiant publication

10.3934/krm.2019045

Métadonnées

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Auteur(s)

Basile, Giada
Dipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
Komorowski, Tomasz
Institut of Mathematics - Polish Academy of Sciences [PAN]
Olla, Stefano

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Résumé (EN)

We consider a linear phonon Boltzmann equation with a reflecting/transmitting/absorbing interface. This equation appears as the Boltzmann-Grad limit for the energy density function of a harmonic chain of oscillators with inter-particle stochastic scattering in the presence of a heat bath at temperature T in contact with one oscillator at the origin. We prove that under the diffusive scaling the solutions of the phonon equation tend to the solution ρ(t, y) of a heat equation with the boundary condition ρ(t, 0) ≡ T .