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The local Cauchy problem for ionized magnetized reactive gas mixtures

โœ Scribed by Vincent Giovangigli; Benjamin Graille

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
266 KB
Volume
28
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

We investigate a system of partial di erential equations modelling ionized magnetized reactive gas mixtures. In this model, dissipative uxes are anisotropic linear combinations of uid variable gradients and also include zeroth-order contributions modelling the direct e ect of electromagnetic forces. There are also gradient dependent source terms like the conduction current in the Maxwell-Ampere equation. We introduce the notion of partial symmetrizability and that of entropy for such systems of partial di erential equations and establish their equivalence. By using entropic variables, we recast the system into a partially normal form, that is, in the form of a quasilinear partially symmetric hyperbolic-parabolic system. Using a result of Vol'Pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution.

๐Ÿ“œ SIMILAR VOLUMES

The local Cauchy problem for multicompon
The local Cauchy problem for multicomponent reactive flows in full vibrational non-equilibrium
โœ Vincent Giovangigli; Marc Massot ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 211 KB

## Communicated by J. C. Nedelec 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 usin