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Article Dans Une Revue Kinetic and Related Models Année : 2019

DIFFUSION LIMIT FOR A KINETIC EQUATION WITH A THERMOSTATTED INTERFACE

Résumé

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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Dates et versions

hal-02059831 , version 1 (06-03-2019)
hal-02059831 , version 2 (28-04-2019)

Identifiants

Citer

Giada Basile, Tomasz Komorowski, Stefano Olla. DIFFUSION LIMIT FOR A KINETIC EQUATION WITH A THERMOSTATTED INTERFACE. Kinetic and Related Models , 2019, 12 (5), pp.1185-1196. ⟨10.3934/krm.2019045⟩. ⟨hal-02059831v2⟩
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