Exact solution of the weakly evaporation problem for the Boltzmann equation with BGK operator collision

Exact solution of the Boltzmann equation with BGK collision operator in weak evaporation problem from plate surface is obtained. Generalized eigenvectors and eigenvalues of charactetistic equation are found. The theorem about expansion of the solution by eigenvectors is proved. The proof reduced to vector Riemann–Hubert boundary value problem with matrix coefficient. Canonical factor-matrix with normal form at infinity is used.