| Abstract: | An exact solution to the model Boltzmann equation with Bhatnagar-Gross-Krook (BGK) collision operator is obtained in the problems of weak evaporation and temperature and density jumps of a rarefied gas in a half-space. Case's method is used to find generalized eigenvectors of the corresponding characteristic equation. An existence and uniqueness theorem for the solution of the posed problems with boundary conditions on a flat surface and far from it is proved. For this, we develop a formalism of diagonalization and factorization of the vector Riemann-Hilbert boundary-value problem with matrix coefficient whose diagonalizing matrix has branch points in the complex plane.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–171, January–February, 1992. |
