Fractional diffusion limit of a linear Boltzmann model with reflective boundaries in a half-space

Abstract

We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show uniqueness of weak solutions to the associated non-local diffusion equation. This paper extends previous results of L. Cesbron, A. Mellet and M. Puel [5] on the same kinetic model with diffusive boundary conditions