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Rigorous solution to the extended kinetic equations for homogeneous gas mixtures

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Book cover Mathematical Aspects of Fluid and Plasma Dynamics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1460))

Abstract

The paper deals with a recently introduced extended kinetic theory for gas mixtures. Such a generalization is aimed at accounting for effects of removal, generation and source, as well as for the presence of a background medium. These physical effects are modeled by suitable gain and loss terms into the set of Boltzmann equations governing the gas distribution functions. The outstanding work done for the search of exact or rigorous analytical solutions to the standard Boltzmann equation in the space homogeneous case and for Maxwell scattering models is reviewed. It is then shown how the previous results can be generalized to treat also gas mixtures in the extended version. In particular, in spite of the nonlinearities, a Fourier transform technique, with suitably defined generating functions, leads to a hierarchy of moment equations solvable in cascade, and a series reconstruction of the distribution functions, converging in an appropriate Hilbert space, follows then by resorting to a Bobylev transformation. Finally, the role played by the theory of dynamical systems in extended kinetic theory is discussed, and some examples of application are presented and commented on.

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Authors and Affiliations

  1. Department of Mathematics, University of Bari, Via G.Fortunato, 70125, Bari, Italy

    Giampiero Spiga

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  1. Giampiero Spiga
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Giuseppe Toscani Vinicio Boffi Salvatore Rionero

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© 1991 Springer-Verlag

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Spiga, G. (1991). Rigorous solution to the extended kinetic equations for homogeneous gas mixtures. In: Toscani, G., Boffi, V., Rionero, S. (eds) Mathematical Aspects of Fluid and Plasma Dynamics. Lecture Notes in Mathematics, vol 1460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091369

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  • DOI: https://doi.org/10.1007/BFb0091369

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  • Print ISBN: 978-3-540-53545-4

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