Fractional diffusion limit of a linear Boltzmann model with reflective boundaries in a half-space
Ludovic Cesbron · Kinetic and Related Models · 2023
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 in a spatially bounded domain and show uniqueness of weak solution to the associated non-local diffusion equation.