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A variational principle for boundary value problems in kinetic theory

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Abstract

A variational principle which applies directly to the integrodifferential form of the linearized Boltzmann equation is introduced. Extremely general boundary conditions and collision terms are allowed. For a class of interesting problems, the value of the functional to be varied is shown to be closely related to quantities of great physical interest. The formalism is applied to the treatment of plane Couette flow for different forms of the collision term (BGK model, rigid spheres, Maxwell's molecules).

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Authors and Affiliations

  1. Applicazioni e Ricerche Scientifiche, S.p.A., Milano

    Carlo Cercignani

  2. Politecnico di Milano, Milano, Italy

    Carlo Cercignani

Authors
  1. Carlo Cercignani
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Additional information

Research sponsored by the Air Force Office of Scientific Research under contract F 61(052)-68-C-0020, through the European Office of Aerospace Research, OAR, United States Air Force.

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Cercignani, C. A variational principle for boundary value problems in kinetic theory. J Stat Phys 1, 297–311 (1969). https://doi.org/10.1007/BF01007482

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  • DOI: https://doi.org/10.1007/BF01007482

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