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On diffuse reflection at the boundary for the Boltzmann equation and related equations. (English) Zbl 0839.76073
Summary: The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a “DiPerna-Lions framework” with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in an \(L^\infty\) framework.

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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