# Global renormalized solutions to reaction-cross-diffusion systems

Source: [Global renormalized solutions to reaction-cross-diffusion systems](<https://www.sota2.com/research/paper/68fa54491e209131ce98a81d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:56:32.194Z

Authors: Xiuqing Chen, Ansgar J\\"ungel

Published: 2017-11-04T16:51:18.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1711.01463>)

[PDF](<https://arxiv.org/pdf/1711.01463.pdf>)