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

Xiuqing Chen; Ansgar Jüngel

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arXiv · 1805.02950

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

Xiuqing Chen·Ansgar Jüngel

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Abstract

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.

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BibTeX RIS

Xiuqing Chen, Ansgar Jüngel. 2018-05-08. Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems. https://arxiv.org/abs/1805.02950

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