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.
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Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–171, January–February, 1992.
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Dolgosheina, E.B., Latyshev, A.V. & Yushkanov, A.A. Exact solutions of model BGK Boltzmann equation in temperature jump and weak evaporation problems. Fluid Dyn 27, 122–128 (1992). https://doi.org/10.1007/BF01054184
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DOI: https://doi.org/10.1007/BF01054184