Perturbative global solutions of a large class of cross diffusion systems in any dimension
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911787169873920 |
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| author | Desvillettes, L Moussa, A |
| author_facet | Desvillettes, L Moussa, A |
| contents | This article focuses on a large family of cross-diffusion systems of the form $\partial$ t U-$Δ$A(U) = 0, in dimension d $\in$ N * , and where U $\in$ R 2. We show that under natural conditions on the nonlinearity A, those systems have a unique smooth (nonnegative for all components) solution when the initial data are small enough in a suitable norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbative global solutions of a large class of cross diffusion systems in any dimension Desvillettes, L Moussa, A Analysis of PDEs This article focuses on a large family of cross-diffusion systems of the form $\partial$ t U-$Δ$A(U) = 0, in dimension d $\in$ N * , and where U $\in$ R 2. We show that under natural conditions on the nonlinearity A, those systems have a unique smooth (nonnegative for all components) solution when the initial data are small enough in a suitable norm. |
| title | Perturbative global solutions of a large class of cross diffusion systems in any dimension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.00391 |