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The local Cauchy problem for multicomponent reactive flows in full vibrational non‐equilibrium
Author(s) -
Giovangigli Vincent,
Massot Marc
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199810)21:15<1415::aid-mma2>3.0.co;2-d
Subject(s) - uniqueness , mathematics , bounded function , conservation law , entropy (arrow of time) , initial value problem , mathematical analysis , cauchy problem , cauchy distribution , formalism (music) , polyatomic ion , thermodynamics , physics , ion , musical , art , quantum mechanics , visual arts
We consider reactive mixtures of dilute polyatomic gases in full vibrational non‐equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic–parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.