Geodesic
The Method of Singular Equations in Boundary Value Problems in Kinetic Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 437-454

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We develop a new effective method for solving boundary value problems in kinetic theory. The method permits solving boundary value problems for mirror and diffusive boundary conditions with an arbitrary accuracy and is based on the idea of reducing the original problem to two problems of which one has a diffusion boundary condition for the reflection of molecules from the wall and the other has a mirror boundary condition. We illustrate this method with two classical problems in kinetic theory: the Kramers problem (isothermal slip) and the thermal slip problem. We use the Bhatnagar–Gross–Krook equation (with a constant collision frequency) and the Williams equation (with a collision frequency proportional to the molecular velocity).
Keywords: boundary value problem, kinetic equation, Kramers problem, thermal slip problem
Mots-clés : isothermal slip coefficient, thermal slip coefficient. 
@article{TMF_2005_143_3_a8,
     author = {A. V. Latyshev and A. A. Yushkanov},
     title = {The {Method} of {Singular} {Equations} in {Boundary} {Value} {Problems} in {Kinetic} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {437--454},
     publisher = {mathdoc},
     volume = {143},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a8/}
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A. V. Latyshev; A. A. Yushkanov. The Method of Singular Equations in Boundary Value Problems in Kinetic Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 437-454. http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a8/