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References
M. Abramowitz, Evaluation of the integral \( \int_0^\infty {e^{ - u^2 - x/u} du} \) , J. Math. Phys. 32, 188–192 (1953).
M. Abramowitz and I.A. Stegun, Handbook of mathematical functions, Applied Mathematical Series, National Bureau of Standards, Washington (1964).
P. Andries, P. Le Tallec, J.P. Perlat, and B. Perthame, The Gaussian-BGK model of Boltzmann equation with small Prandtl number, Euro. J. of Mechanics B 19, 813–830 (2000).
P.L. Bhatnagar, E.P. Gross and M. Krook, A model for collision processes in gases. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511–525 (1954).
C. Cercignani, The Boltzmann equation and its applications, (Springer, New York, 1988).
C. Cercignani, Mathematical Methods in Kinetic Theory, (Plenum Press, New York, 1990).
C. Cercignani, On the general solution of the steady linearized Boltzmann equation, in Rarefied Gas Dynamics, M. Becker and M. Fiebig eds., Vol. I, A.9-1-11, DFLVR Press, Porz-Wahn (1974).
C. Cercignani, Plane Couette flow according to the method of elementary solutions, J. Math. Anal. Appl. 11, 93–101 (1965).
C. Cercignani, A variational principle for boundary value problems in kinetic theory, J. Stat. Phys. 1, 297–311 (1969).
C. Cercignani, Plane Poiseuille flow and Knudsen minimum effect, in Rarefied Gas Dynamics, J. A. Laurman ed., Vol II, 92–101, Academic Press, New York (1963).
C. Cercignani, Plane Poiseuille flow according to the method of elementary solutions, J. Math. Anal. Appl. 12, 254–262 (1965)
C. Cercignani and A. Daneri, Flow of a rarefied gas between two parallel plates, Jour. Appl. Phys. 34, 3509–3513 (1963).
C. Cercignani and C. D. Pagani, Variational approach to boundary-value problems in kinetic theory, Phys. of Fluids 9, 1167–1173 (1966).
C. Cercignani and G. Tironi, Nonlinear heat transfer between two parallel plates at large temperature ratios, in Rarefied Gas Dynamics, C.L. Brundin, Ed., Vol. I, 441–453, Academic Press, New York (1967).
L.H. Holway, Jr., Approximation procedures for kinetic theory, Ph.D. Thesis, Harvard (1963).
M. Knudsen, Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren, Ann. der Physik, 28, 75–130 (1909).
J.L. Lebowitz, H.L. Frisch and E. Helfand, Nonequilibrium distribution functions in a fluid, Phys. Fluids 3, 325–338 (1960).
L. Sirovich, Kinetic modeling of gas mixtures, Phys. Fluids 5, 908–918, (1962).
Y. Sone, S. Takata, and T. Ohwada, Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules, Eur. J. Mech., B: Fluids 9, 273–288 (1990).
P. Welander, On the temperature jump in a rarefied gas, Arkiv Fysik 7, 507–553 (1954).
D.R. Willis, Comparison of kinetic theory analyses of linearized Couette flow, Phys. Fluids, 5, 127–135 (1962).
W. Dong, University of California Report UCRL 3353 (1956).
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(2006). Slow Flows in a Slab. In: Slow Rarefied Flows. Progress in Mathematical Physics, vol 41. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7537-X_5
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