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A steady‐state system in non‐equilibrium thermodynamics including thermal and electrical effects
Author(s) -
Degond Pierre,
Génieys Stéphane,
Jüngel Ansgar
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<1399::aid-mma1>3.0.co;2-#
Subject(s) - thermodynamics , steady state (chemistry) , mathematics , statistical physics , thermal , thermodynamic equilibrium , equilibrium thermodynamics , non equilibrium thermodynamics , physics , chemistry
The steady‐state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet–Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro‐chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.