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arXiv · 1711.01463

Global renormalized solutions to reaction-cross-diffusion systems

Xiuqing Chen·Ansgar Jüngel
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Abstract

The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary 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 semi-definite, but the system possesses a formal gradient-flow or entropy structure. The reaction part includes reversible reactions of mass-action 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.

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Xiuqing Chen, Ansgar Jüngel. 2017-11-04. Global renormalized solutions to reaction-cross-diffusion systems. https://arxiv.org/abs/1711.01463

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