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C. Helmer, A. Jüngel:
"Analysis of Maxwell-Stefan systems for heat conducting fluid mixtures";
in: "ASC Report 9/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 20.

The global-in-time existence of weak solutions to the Maxwell{Stefan{Fourier equations in Fick{Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and and the energy balance equation for the total
energy. The diffusion and heat uxes depend linearly on the gradients of the thermochemical potentials and the gradient of the temperature and include the Soret and Dufour effects. The cross-diffusion system exhibits an entropy structure, which originates from
the consistent thermodynamic modeling. The lack of positive definiteness of the diffusion matrix is compensated by the fact that the total mass density is constant in time. The entropy estimate also allows for the proof of the a.e. positivity of the partial mass densities and temperature.

Fick{Onsager cross-diffusion equations, Maxwell{Stefan systems, fluid mixtures, existence of solutions, positivity

http://www.asc.tuwien.ac.at/preprint/2020/asc09x2020.pdf