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Diffusion limit for a kinetic equation with a thermostatted interface

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
Journal name
Kinetic & Related Models
Volume
12
Number
5
Publisher
AIMS - American Institute of Mathematical Sciences
Published in
Paris
Pages
1185-1196
Publication identifier
Metadata
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Author(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 cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (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 .
Subjects / Keywords
Diffusion limit; thermostatted boundary conditions