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

Ludovic Cesbron

doi:10.3934/krm.2023033

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2024, Volume 17, Issue 4: 577-605. Doi: 10.3934/krm.2023033

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

Ludovic Cesbron

Laboratoire AGM, Département de Mathématiques, CY Cergy Paris Université, France

Received: October 2022

Early access: October 2023

Published: August 2024

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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 in a spatially bounded domain and show uniqueness of weak solution to the associated non-local diffusion equation.

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Mathematics Subject Classification: Primary: 82B40, 35B40; Secondary: 26A33, 35S16.

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