On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of Gases

Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in half space. At boundary of space, it is assumed that contact its condensed phase. The present paper discusses existence and uniqueness uniformly decaying layer type solution this situation, vicinity Maxwellian equilibrium zero bulk velocity, same temperature as phase, whose pressure saturating vapor at interface. This problem has been extensively studied first by Y. Sone, K. Aoki their collaborators, means careful numerical simulations. See section 2 [C. Bardos, F. Golse, Sone: J. Stat. Phys. 124 (2006), 275-300] very detailed presentation these works. More recently T.-P. Liu S.-H. Yu [Arch. Rational Mech. Anal. 209 (2013), 869-997] have proposed an extensive mathematical strategy to handle problems numerically group. offers alternative, possibly simpler proof one results discussed [T.P. Liu, Yu, loc. cit.]