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Article Dans Une Revue Annals of Probability Année : 2020

Fractional diffusion limit for a kinetic equation with an interface *

Résumé

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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Dates et versions

hal-02139751 , version 1 (25-05-2019)

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Domaine public

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Tomasz Komorowski, Stefano Olla, Lenya Ryzhik. Fractional diffusion limit for a kinetic equation with an interface *. Annals of Probability, 2020, 48 (5), pp.2290--2322. ⟨10.1214/20-AOP1423⟩. ⟨hal-02139751⟩
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