Global existence for a system without self-diffusion and different mobilities
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917413304401920 |
|---|---|
| author | Elbar, Charles |
| author_facet | Elbar, Charles |
| contents | We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation scheme, yields existence of global weak solutions. More precisely, we introduce a notion of \textit{admissible approximation sequence} and show that any such sequence admits a subsequence converging to a weak solution of the system. The strategy relies on entropy estimates and the div--curl lemma, in the framework of Young measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14775 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global existence for a system without self-diffusion and different mobilities Elbar, Charles Analysis of PDEs 35K65, 35B40, 35Q92, 35K55, 35D30 We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation scheme, yields existence of global weak solutions. More precisely, we introduce a notion of \textit{admissible approximation sequence} and show that any such sequence admits a subsequence converging to a weak solution of the system. The strategy relies on entropy estimates and the div--curl lemma, in the framework of Young measures. |
| title | Global existence for a system without self-diffusion and different mobilities |
| topic | Analysis of PDEs 35K65, 35B40, 35Q92, 35K55, 35D30 |
| url | https://arxiv.org/abs/2604.14775 |