Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions
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| Format: | Preprint |
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2025
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| _version_ | 1866916912627187712 |
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| author | Bouton, Hector Desvillettes, Laurent Dietert, Helge |
| author_facet | Bouton, Hector Desvillettes, Laurent Dietert, Helge |
| contents | We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions. A key part is the independent careful study of the parabolic equation $a\partial_t w - Δw = f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption $\partial_tw \ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_08186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions Bouton, Hector Desvillettes, Laurent Dietert, Helge Analysis of PDEs We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions. A key part is the independent careful study of the parabolic equation $a\partial_t w - Δw = f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption $\partial_tw \ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry. |
| title | Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.08186 |