Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911377945264128 |
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| author | De Nitti, Nicola Zamponi, Nicola |
| author_facet | De Nitti, Nicola Zamponi, Nicola |
| contents | We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the initial-boundary value problem and analyze the convergence of the solutions to equilibrium via relative entropy methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics De Nitti, Nicola Zamponi, Nicola Analysis of PDEs Mathematical Physics 35K40, 35R11, 35A01, 35A02, 35B40 We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the initial-boundary value problem and analyze the convergence of the solutions to equilibrium via relative entropy methods. |
| title | Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics |
| topic | Analysis of PDEs Mathematical Physics 35K40, 35R11, 35A01, 35A02, 35B40 |
| url | https://arxiv.org/abs/2407.19824 |