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

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.