English

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.

Keywords

Cite

@article{arxiv.1710.01623,
  title  = {Cross-diffusion systems with entropy structure},
  author = {Ansgar Jüngel},
  journal= {arXiv preprint arXiv:1710.01623},
  year   = {2017}
}