Anomalous diffusion limit for a kinetic equation with a thermostatted interface

We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-absorption condition at the interface. Both the coefficient describing the probability of absorption and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique...

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Bibliographic Details
Published in:arXiv.org 2022-09
Main Authors: Bogdan, Krzysztof, Komorowski, Tomasz, Marino, Lorenzo
Format: Article
Language:English
Subjects:
Absorption
Kinetic equations
Thermodynamics
Online Access:Get full text
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Summary:We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-absorption condition at the interface. Both the coefficient describing the probability of absorption and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov equation for a symmetric stable process, which is reflected, or transmitted while crossing the interface and is killed upon the first hitting of the interface. The results of the paper are related to the work in [KOR20], where the case of a non-degenerate probability of absorption has been considered.
ISSN:2331-8422