X. Chen, A. Jüngel:

"Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems";

in: "ASC Report 11/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 30.

The weak-strong uniqueness for solutions to reaction-cross-diﬀusion systems in a bounded domain with no-ﬂux boundary conditions is proved. The system generalizes the Shigesada-Kawasaki-Teramoto population model to an arbitrary number of species. The diﬀusion matrix is neither symmetric nor positive deﬁnite, but the system possesses a formal gradient-ﬂow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modiﬁed by suitable cutoﬀ functions.

Shigesada-Kawasaki-Teramoto model, renormalized solution, weak-strong uniqueness, relative entropy

http://www.asc.tuwien.ac.at/preprint/2018/asc11x2018.pdf

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