| Abstract: | An exact solution of the ellipsoidal-statistical model Boltzmann equation is constructed. The problem of the temperature jump in a rarefied gas is considered by way of illustration. By expanding the distribution function in two orthogonal directions the problem is reduced to the solution of a vector transport equation with polynomial boundary conditions. The Case approach reduces the equation to a characteristic equation for which generalized eigenvectors and eigenvalues are found. A theorem of existence and uniqueness of the solution, represented in the form of an expansion in eigenvectors, is proved. The proof reduces to solving a Riemann-Hilbert vector boundary-value problem with a matrix coefficient whose diagonalizing matrix has branch points in the complex plane. The value of the temperature jump is found from the conditions of solvability of the boundary-value problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 151–164, March–April, 1992. |
