Global renormalized solutions to reaction-cross-diffusion systems
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.
Cite
@article{arxiv.1711.01463,
title = {Global renormalized solutions to reaction-cross-diffusion systems},
author = {Xiuqing Chen and Ansgar Jüngel},
journal= {arXiv preprint arXiv:1711.01463},
year = {2017}
}