Work

Cross-diffusion systems with entropy structure

Year: 2017

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1710.01623

Author: Jüngel, Ansgar

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Awards: Analysis of diffusion models for multi-species systems, Derivation and analysis of cross-diffusion systems, Dissipation and dispersion in differential equations

OpenAlex ID: W2762039470

Cites:

Cited by: 12

Related to: 10