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Diffusion limit for a kinetic equation with a thermostatted interface

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Date
2019
Publisher city
Paris
Dewey
Probabilités et mathématiques appliquées
Sujet
Diffusion limit; thermostatted boundary conditions
Journal issue
Kinetic & Related Models
Volume
12
Number
5
Publication date
2019
Article pages
1185-1196
Publisher
AIMS - American Institute of Mathematical Sciences
DOI
http://dx.doi.org/10.3934/krm.2019045
URI
https://basepub.dauphine.fr/handle/123456789/18572
Collections
  • CEREMADE : Publications
Metadata
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Author
Basile, Giada
92732 Dipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
Komorowski, Tomasz
89537 Institut of Mathematics - Polish Academy of Sciences [PAN]
Olla, Stefano
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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 .

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