  Half-space problems in the kinetic theory of gases are of great importance in
the study of the asymptotic behavior of solutions of boundary value problems
for the Boltzmann equation for small Knudsen numbers. In this work a generally
formulated half-space problem, based on generalizations of stationary
half-space problems in one spatial variable for the Boltzmann equation - for
hard-sphere models of monatomic single species and multicomponent mixtures - is
considered. The number of conditions on the indata at the interface needed to
obtain well-posedness is investigated. Exponential fast convergence is obtained
"far away" from the interface. In particular, the exponential decay at regime
transitions - where the number of conditions on the indata needed to obtain
well-posedness changes - for linearized kinetic half-space problems related to
the half-space problem of evaporation and condensation in kinetic theory are
considered. The regime transitions correspond to the transition between
subsonic and supersonic evaporation/condensation, or the transition between
evaporation and condensation. Near the regime transitions, slowly varying modes
might occur, preventing uniform exponential speed of convergence there. By
imposing extra conditions on the indata at the interface, the slowly varying
modes can be eliminated near a regime transition, giving rise to uniform
exponential speed of convergence near the regime transition.
  Values of the velocity of the flow at the far end, for which regime
transitions take place are presented for some particular variants of the
Boltzmann equation: for monatomic and polyatomic single species and mixtures,
and the quantum variant for bosons and fermions.
