A gradient flow approach to linear Boltzmann equations

TL;DR

This paper presents a novel gradient flow formulation of linear Boltzmann equations and derives a diffusion equation from it under diffusive scaling, providing a new perspective on these equations.

Contribution

It introduces a gradient flow approach to linear Boltzmann equations and derives a diffusion limit using this framework, which is a new methodological contribution.

Findings

Gradient flow formulation of linear Boltzmann equations

Derivation of diffusion equation from Boltzmann equations under diffusive scaling

Provides a new analytical framework for kinetic equations

Abstract

We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.