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Solutions for Models of Chemically Reacting Compressible Mixtures

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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Abstract

The mathematical modeling of chemically reacting mixtures is investigated. The governing equations, which may be split between conservation equations, thermochemistry, and transport fluxes, are presented as well as typical simplifications often encountered in the literature. The hyperbolic–parabolic structure of the resulting system of partial differential equations is analyzed using symmetrizing variables. The Cauchy problem is discussed for the full system derived from the kinetic theory of gases as well as relaxation toward chemical equilibrium fluids in the fast chemistry limit. The situations of traveling waves and reaction–diffusion systems are also addressed.

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  1. CMAP-CNRS, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Vincent Giovangigli

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  1. Vincent Giovangigli
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  1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan

    Yoshikazu Giga

  2. Université de Toulon IMATH, Toulon, France

    Antonín Novotný

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Giovangigli, V. (2018). Solutions for Models of Chemically Reacting Compressible Mixtures. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_73

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