  We construct center manifolds for a class of degenerate evolution equations
including the steady Boltzmann equation and related kinetic models,
establishing in the process existence and behavior of small-amplitude kinetic
shock and boundary layers. Notably, for Boltzmann's equation, we show that
elements of the center manifold decay in velocity at near-Maxwellian rate, in
accord with the formal Chapman-Enskog picture of near-equilibrium ow as
evolution along the manifold of Maxwellian states, or Grad moment approximation
via Hermite polynomials in velocity. Our analysis is from a classical dynamical
systems point of view, with a number of interesting modifications to
accommodate ill-posedness of the underlying evolution equation.
