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X. Chen, A. Jüngel:
"A note on the uniqueness of weak solutions to a class of cross-diffusion styles";
in: "ASC Report 11/2017", Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 14.

The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equa-tions include cross-diffusion and drift terms and are coupled selfconsistently to the Poisson equation. The model class contains special cases of the Maxwell-Stefan equations for gas mixtures, generalized Shigesada-Kawasaki-Teramoto equations for population dynamics, and volume-filling models for ion transport. The uniqueness proof is based on a combination of the H 1 technique and the entropy method of Gajewsk

Strongly coupled parabolic systems, uniqueness of weak solutions, entropymethod, Maxwell-Stefan systems, population dynamics, volume filling

http://www.asc.tuwien.ac.at/preprint/2017/asc11x2017.pdf