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We construct stable manifolds for a class of degenerate evolution equationsincluding the steady Boltzmann equation, establishing in the processexponential decay of associated kinetic shock and boundary layers to theirlimiting equilibrium states. Our analysis is from a classical dynamical systemspoint of view, but with a number of interesting modifications to accomodateill-posedness with respect to the Cauchy problem of the underlying evolutionequation.

Stable manifolds for a class of degenerate evolution equations and exponential decay of kinetic shocks