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arXiv · 1905.10586

Fractional diffusion limit for a kinetic equation with an interface

Tomasz Komorowski·Stefano Olla·Lenya Ryzhik
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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.

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Tomasz Komorowski, Stefano Olla, Lenya Ryzhik. 2019-05-25. Fractional diffusion limit for a kinetic equation with an interface. https://arxiv.org/abs/1905.10586

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