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Symmetry of the Linearized Boltzmann Equation and Its Application

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Abstract

A symmetric relation of macroscopic quantities between two different steady problems of the linearized Boltzmann equation is derived. A few applications to half-space problems are presented first. Then, for the gas in bounded or unbounded domains such that solid bodies or condensed phases are confined in a finite region, general representations of the mass, momentum, and heat fluxes through the boundary (possibly at a point on or on a part of it) are derived from the symmetric relation linked to the separability of boundary data. This result implies a reduction of the original problem to a single elemental problem in the same domain, as far as the fluxes are concerned. Many applications are also presented.

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  1. Department of Mechanical Engineering and Science, (also Advanced Research Institute of Fluid Engineering and Science), Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan

    Shigeru Takata

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Takata, S. Symmetry of the Linearized Boltzmann Equation and Its Application. J Stat Phys 136, 751–784 (2009). https://doi.org/10.1007/s10955-009-9793-2

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  • DOI: https://doi.org/10.1007/s10955-009-9793-2

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