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On the nonlinear, spatially homogeneous Boltzmann equation with an external source: Exact generating functions for all moments

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Abstract

A moment method is applied to a model Boltzmann equation including an isotropic external source. The associated infinite system of first-order differential equations for the moments is solved exactly to the extent that analytical expressions for the generating function of the moments are derived. Due to a consequent application of Lie group methods the resulting functions are of the similarity form. Certain restrictions upon the shape of the source term arising from the solution strategy are discussed.

Zusammenfassung

Eine Momentenmethode wird angewandt auf eine Modell-Boltzmanngleichung mit einem isotropen Quellterm. Das zugehörige unendliche System von Differentialgleichungen 1. Ordnung für die Momente wird exakt gelöst in dem Sinne, daß analytische Ausdrücke für die Erzeugende Funktion der Momente angegeben werden. Aufgrund einer konsequenten Anwendung von Lie-Gruppenmethoden nehmen die Lösungen Similarity-Form an. Durch die Lösungsstrategie ergeben sich bestimmte Einschränkungen für die zulässigen Quellterme.

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Authors and Affiliations

  1. Dept. of Mathematical Physics, University of Ulm, D-7900, Ulm, Germany

    G. Dukek & D. Rupp

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  1. G. Dukek
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  2. D. Rupp
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Dukek, G., Rupp, D. On the nonlinear, spatially homogeneous Boltzmann equation with an external source: Exact generating functions for all moments. Journal of Applied Mathematics and Physics (ZAMP) 37, 837–848 (1986). https://doi.org/10.1007/BF00953675

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  • DOI: https://doi.org/10.1007/BF00953675

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