Anomalous diffusion limit for a kinetic equation with a thermostatted interface

• 成果类型: Article
• 署名作者: Bogdan, Krzysztof; Komorowski, Tomasz; Marino, Lorenzo
• 署名单位: Wroclaw University of Science & Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Institut Polytechnique de Paris; ENSTA Paris
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01251-3
• 发表日期: 2024
• 页码: 721-769
• 关键词: harmonic-oscillators; THEOREMS; chain

摘要

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 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.