Quantitative tauberian approach to collisionless transport equations with diffuse boundary operators

TL;DR

This paper develops a spectral method to analyze the long-term behavior of collisionless transport equations with diffuse boundary conditions, establishing stability and convergence rates to equilibrium using advanced harmonic analysis techniques.

Contribution

It introduces a spectral approach combined with a quantitative Ingham theorem to derive algebraic convergence rates for collisionless transport semi-groups with diffuse boundary operators.

Findings

Established strong stability of invariant densities.

Derived algebraic convergence rates to equilibrium.

Applied spectral methods to collisionless transport equations.

Abstract

This paper gives a spectral approach to time asymptotics of collisionless transport semi-groups with general diffuse boundary operators. The strong stability of the invariant density is derived from the classical Ingham theorem. A recent quantitative version of this theorem provides algebraic rates of convergence to equilibrium.