Analytical solution of the strong evaporation (condensation) problem (Q1339630)

An exact solution of the model Boltzmann equation with BGK (Bhatnagar-- Gross--Krook) collision operator is obtained in the problem of strong evaporation (condensation) from a plane surface. The generalized eigenvectors of the corresponding characteristic equation are found. The existence and uniqueness of the expansion of the solution in eigenvectors of the continuous and discrete spectra are demonstrated. This expansion reduces to a vector Riemann-Hilbert boundary value problem with matrix coefficient. An apparatus for the diagonalization and factorization of the boundary value problem coefficient is developed.