Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01819 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910097156866048 |
|---|---|
| author | Dus, Mathias Jüngel, Ansgar |
| author_facet | Dus, Mathias Jüngel, Ansgar |
| contents | A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations via the Jordan-Kinderlehrer-Otto scheme. Compactness of the approximate sequence is obtained using either the flow interchange technique or the five gradient inequality. These methods are illustrated for both parabolic and hyperbolic-parabolic Busenberg-Travis systems, as well as for several of their variants. This paper reviews the results from the literature and discusses additional properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A review of compactness methods for cross-diffusion systems seen as Wasserstein gradient flows Dus, Mathias Jüngel, Ansgar Analysis of PDEs 35K51, 35A15, 76T99 A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations via the Jordan-Kinderlehrer-Otto scheme. Compactness of the approximate sequence is obtained using either the flow interchange technique or the five gradient inequality. These methods are illustrated for both parabolic and hyperbolic-parabolic Busenberg-Travis systems, as well as for several of their variants. This paper reviews the results from the literature and discusses additional properties. |
| title | A review of compactness methods for cross-diffusion systems seen as Wasserstein gradient flows |
| topic | Analysis of PDEs 35K51, 35A15, 76T99 |
| url | https://arxiv.org/abs/2604.01819 |