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E. Daus, L. Desvillettes, A. Jüngel:
"Cross-diffusion systems and fast-reaction limits";
in: "ASC Report 20/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 25.

The rigorous asymptotics from reaction-cross-diffusion systems for three spe-cies with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary conditions. The global existence of very weak (integrable) solutions and the rigorous fast-reaction limit are proved. The limiting system inherits the entropy structure with an entropy that is not the sum of the entropies of the components. Uniform estimates are derived from the entropy inequality and the duality method.

Strongly coupled parabolic systems, reaction-cross-diffusion equations, existence of weak solutions, fast-reaction limit, entropy method, duality metho-

http://www.asc.tuwien.ac.at/preprint/2017/asc20x2017.pdf