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

2020/03/27 by Ludovic Cesbron, Cesbron, Ludovic
Computer Science · Mathematics · #26A33 #35B40 #35S16 #82B40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.12534

openalex publication_date 2020/03/27 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

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.

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