Summary
An exact analytical solution to a simple problem of extended kinetic theory for a spatially inhomogeneous binary gas mixture is determined in this paper by resorting to Lie group theoretical methods. It is shown that there are cases in which the nonlinear evolution equations for the densities allow transformation groups of infinite order, where the corresponding similarity solution actually represents the general solution to the problem. Results are then briefly commented on.
Zusammenfassung
In dieser Abhandlung wird eine exakte analytische Lösung für ein einfaches Problem aus der erweiterten kinetischen Theorie räumlich inhomogener binärer Gasmischungen angegeben. Es wird gezeigt, daß die nichtlinearen Evolutionsgleichungen für die Dichten in bestimmten Fällen Lie-Gruppen von unendlicher Ordnung zulassen. Die zugehörigen Similarity-Lösungen stellen dann allgemeine Lösungen des zugrundeliegenden Problems dar. Die Ergebnisse werden kurz erläutert.
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V. C. Boffi, G. Spiga,Spatially inhomogeneous nonlinear dynamics of a gas mixture, to be published.
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On leave from: Institute of Mathematical Physics, University of Ulm, Oberer Eselsberg, 7900 Ulm, F.R.G.
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Dukek, G., Spiga, G. Similarity solutions in space dependent extended kinetic theory. Z. angew. Math. Phys. 39, 924–930 (1988). https://doi.org/10.1007/BF00945128
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DOI: https://doi.org/10.1007/BF00945128