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Half-space problems in the kinetic theory of gases are of great importance inthe study of the asymptotic behavior of solutions of boundary value problemsfor the Boltzmann equation for small Knudsen numbers. In this work a generallyformulated half-space problem, based on generalizations of stationaryhalf-space problems in one spatial variable for the Boltzmann equation - forhard-sphere models of monatomic single species and multicomponent mixtures - isconsidered. The number of conditions on the indata at the interface needed toobtain well-posedness is investigated. Exponential fast convergence is obtained"far away" from the interface. In particular, the exponential decay at regimetransitions - where the number of conditions on the indata needed to obtainwell-posedness changes - for linearized kinetic half-space problems related tothe half-space problem of evaporation and condensation in kinetic theory areconsidered. The regime transitions correspond to the transition betweensubsonic and supersonic evaporation/condensation, or the transition betweenevaporation and condensation. Near the regime transitions, slowly varying modesmight occur, preventing uniform exponential speed of convergence there. Byimposing extra conditions on the indata at the interface, the slowly varyingmodes can be eliminated near a regime transition, giving rise to uniformexponential speed of convergence near the regime transition.  Values of the velocity of the flow at the far end, for which regimetransitions take place are presented for some particular variants of theBoltzmann equation: for monatomic and polyatomic single species and mixtures,and the quantum variant for bosons and fermions.

Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions