MULTICOMPONENT REACTIVE FLOWS

(I)  SYMMETRIZATION AND LOCAL EXISTENCE

Vincent GIOVANGIGLI and Marc MASSOT
 
Centre de Math\'ematiques Appliqu\'ees

Ecole Polytechnique, 91128 Palaiseau Cedex, France





We consider the equations governing multicomponent reactive flows 
derived from the kinetic theory of dilute polyatomic reactive gas 
mixtures. Using an  entropy function, we derive  a symmetric 
conservative form of the system. In the framework of Kawashima's 
and Shizuta's theory, we recast the resulting system into a 
normal form, that is, in the form of a symmetric
hyperbolic-parabolic composite system. We also characterize all 
normal forms for symmetric systems of conservation laws such that
the nullspace associated with dissipation matrices is invariant.   
Using a result of Vol'pert and Hudjaev, we then  prove the local 
existence of a  bounded smooth solution to the Cauchy problem.

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