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The local Cauchy problem for ionized magnetized reactive gas mixtures
Author(s) -
Giovangigli Vincent,
Graille Benjamin
Publication year - 2005
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/mma.629
Subject(s) - mathematics , uniqueness , partial differential equation , dissipative system , mathematical analysis , bounded function , hyperbolic partial differential equation , ordinary differential equation , parabolic partial differential equation , differential equation , physics , thermodynamics
We investigate a system of partial differential equations modelling ionized magnetized reactive gas mixtures. In this model, dissipative fluxes are anisotropic linear combinations of fluid variable gradients and also include zeroth‐order contributions modelling the direct effect 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 differential 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. Copyright © 2005 John Wiley & Sons, Ltd.