| Abstract: | 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. The matrix diagonalizing the problem coefficient has branch points in the complex plane which depend parametrically on the evaporation (condensation) rateu. The solution of the problem is investigated in terms ofu and the physical characteristics of the evaporation process are described.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 143–155, November–December, 1993. |
