Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

TL;DR

This paper analyzes the hyperbolic scaling limits of linear kinetic models on networks, providing rigorous error estimates for the asymptotic behavior as the Knudsen number approaches zero.

Contribution

It introduces a change of variables that simplifies the coupled system into independent problems and rigorously justifies the asymptotic expansions with error estimates.

Findings

Asymptotic expansions are validated with energy-based error estimates.

The reformulation simplifies analysis of kinetic models on networks.

Results provide rigorous bounds for the hyperbolic limit behavior.

Abstract

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.