Invariant manifolds for a class of degenerate evolution equations and structure of kinetic shock layers

TL;DR

This paper develops dynamical systems methods to analyze the structure of kinetic shock layers in degenerate evolution equations like the Boltzmann and BGK equations, advancing understanding of their stability and asymptotic behavior.

Contribution

It introduces new dynamical systems tools tailored for degenerate evolution equations in kinetic theory, providing insights into shock layer structures.

Findings

Characterization of kinetic shock layer structures

Initial steps toward stability analysis

Application to Boltzmann and BGK equations

Abstract

We describe recent results with A. Pogan developing dynamical systems tools for a class of degenerate evolution equations arising in kinetic theory, including the steady Boltzmann and BGK equations. These yield information on structure of large- and small-amplitude kinetic shocks, the first steps in a larger program toward time-evolutionary stability and asymptotic behavior