A cross-diffusion system with independent drifts and fast diffusion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908584298676224 |
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| author | Elbar, Charles Santambrogio, Filippo |
| author_facet | Elbar, Charles Santambrogio, Filippo |
| contents | We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< α\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with bounded entropy and a mixing condition we prove the existence of global weak solutions. This extends the recent result of Mészáros, Parker from the linear diffusion ($α=1$) to the fast-diffusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A cross-diffusion system with independent drifts and fast diffusion Elbar, Charles Santambrogio, Filippo Analysis of PDEs 35K55, 35K65, 35D30, 35Q92, 92D25 We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< α\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with bounded entropy and a mixing condition we prove the existence of global weak solutions. This extends the recent result of Mészáros, Parker from the linear diffusion ($α=1$) to the fast-diffusion. |
| title | A cross-diffusion system with independent drifts and fast diffusion |
| topic | Analysis of PDEs 35K55, 35K65, 35D30, 35Q92, 92D25 |
| url | https://arxiv.org/abs/2510.07937 |