Cross-diffusion systems with entropy structure
Analysis of PDEs
2017-10-05 v1
Abstract
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diffusion systems. Furthermore, a partial result on the uniqueness of weak solutions is recalled, and some open problems are presented.
Cite
@article{arxiv.1710.01623,
title = {Cross-diffusion systems with entropy structure},
author = {Ansgar Jüngel},
journal= {arXiv preprint arXiv:1710.01623},
year = {2017}
}