Fractional diffusion limit of a linear kinetic equation in a bounded domain

TL;DR

This paper derives a fractional diffusion limit for a kinetic transport model with boundary conditions in bounded domains, highlighting differences in nonconvex geometries and linking to stochastic jump processes.

Contribution

It introduces a fractional diffusion limit in bounded domains with boundary conditions, extending previous models to nonconvex geometries.

Findings

Fractional diffusion limit derived for bounded domains.

Differences identified in nonconvex domain cases.

Connection established to stochastic jump processes.

Abstract

A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs from standard formulations. It can be interpreted as the forward Kolmogorow equation of a stochastic process with jumps along straight lines, remaining inside the domain.