FRACTIONAL DIFFUSION LIMIT FOR A KINETIC EQUATION WITH AN INTERFACE

• 成果类型: Article
• 署名作者: Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1423
• 发表日期: 2020
• 页码: 2290-2322
• 关键词: theorems

摘要

We consider the limit of a linear kinetic equation with reflection-transmission-absorption at an interface and with a degenerate scattering kernel. The equation arises 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.