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arXiv · 1903.02621

Diffusion limit for a kinetic equation with a thermostatted interface

Giada Basile·Tomasz Komorowski·Stefano Olla
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Abstract

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 $ρ(t,0)\equiv T$.

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Giada Basile, Tomasz Komorowski, Stefano Olla. 2019-03-06. Diffusion limit for a kinetic equation with a thermostatted interface. https://arxiv.org/abs/1903.02621

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