Author:
Bogdan Krzysztof,Komorowski Tomasz,Marino Lorenzo
Abstract
AbstractWe consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing 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 Komorowski et al. (Ann Prob 48:2290–2322, 2020), where the case of a non-degenerate probability of killing has been considered.
Funder
Narodowe Centrum Nauki
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
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