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X. Chen, A. Jüngel:
"Global renormalized solutions to reaction-cross-diffusion systems";
in: "ASC Report 23/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 30.

The global-in-time existence of renormalized solutions to reaction-cross-diffusion systems for an arbitrary number of variables in bounded domains with no-flux bound-ary conditions is proved. The cross-diffusion part describes the segregation of population species and is a generalization of the Shigesada-Kawasaki-Teramoto model. The diffusion matrix is not diagonal and generally neither symmetric nor positive semidefinite, but the system possesses a formal gradient-flow or entropy structure. The reaction part includes reversible reactions of massaction kinetics and does not obey any growth condition. The existence result generalizes both the condition on the reaction part required in the boundedness-by-entropy method and the proof of J. Fischer for reaction-diffusion systems with diagonal diffusion matrices.

Reaction-cross-diffusion systems, renormalized solutions, gradient flow, entropymethod, population model, defect measure.

http://www.asc.tuwien.ac.at/preprint/2017/asc23x2017.pdf