Anomalous diffusion limit for a kinetic equation with a thermostatted interface
Krzysztof Bogdan,
Tomasz Komorowski,
Lorenzo Marino
Abstract:We 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 upo… Show more
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