Fractional diffusion limit for a kinetic equation with an interface
Probability
2019-05-28 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We consider the limit of a linear kinetic equation, with reflection-transmission-absorption at an interface, with a degenerate scattering kernel. The equation arise from a microscopic chain of oscillators in contact with a heat bath. In the absence of the interface, the solutions exhibit a superdiffusive behavior in the long time limit. With the interface, the long time limit is the unique solution of a version of the fractional in space heat equation, with reflection-transmission-absorption at the interface. The limit problem corresponds to a certain stable process that is either absorbed, reflected, or transmitted upon crossing the interface.
Keywords
Cite
@article{arxiv.1905.10586,
title = {Fractional diffusion limit for a kinetic equation with an interface},
author = {Tomasz Komorowski and Stefano Olla and Lenya Ryzhik},
journal= {arXiv preprint arXiv:1905.10586},
year = {2019}
}