论文标题
具有恒温界面的动力学方程的异常扩散极限
Anomalous diffusion limit for a kinetic equation with a thermostatted interface
论文作者
论文摘要
我们考虑在界面处具有反射 - 传播吸收条件的缩放线性动力学方程的溶液限制。描述吸收概率的系数和散射核退化。我们证明，长时间的大空间极限是空间热方程中分数版本的独特解决方案，它与Kolmogorov方程相对应，用于对称稳定过程，该过程反映或越过界面时反映或传输并在界面的第一次命中时被杀死。本文的结果与[Kor20]中的工作有关，在[KOR20]中，已经考虑了非分类吸收概率的情况。
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.
