Anomalous diffusion limit for a linear Boltzmann equation with external force field

Author:

Aceves-Sanchez Pedro1,Mellet Antoine2

Affiliation:

1. Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

2. Department of Mathematics, University of Maryland, College Park, MD 20742, USA

Abstract

This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to investigate the case where a given acceleration field is present. The main result of this paper shows that for an appropriate scaling of the acceleration field, the usual fractional diffusion equation is supplemented by an advection term. Both the critical and supercritical case are considered.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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