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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.20188 |
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| _version_ | 1866909443831103488 |
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| author | Dębiec, Tomasz Schmidtchen, Markus |
| author_facet | Dębiec, Tomasz Schmidtchen, Markus |
| contents | Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlocal approximation of an anisotropic cross-diffusion system Dębiec, Tomasz Schmidtchen, Markus Analysis of PDEs Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution. |
| title | Nonlocal approximation of an anisotropic cross-diffusion system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.20188 |