Gradient flows of interacting Laguerre cells as discrete porous media flows
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910899250397184 |
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| author | Natale, Andrea |
| author_facet | Natale, Andrea |
| contents | We study a class of discrete models in which a collection of particles evolves in time following the gradient flow of an energy depending on the cell areas of an associated Laguerre (i.e. a weighted Voronoi) tessellation. We consider the high number of cell limit of such systems and, using a modulated energy argument, we prove convergence towards smooth solutions of nonlinear diffusion PDEs of porous medium type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gradient flows of interacting Laguerre cells as discrete porous media flows Natale, Andrea Numerical Analysis We study a class of discrete models in which a collection of particles evolves in time following the gradient flow of an energy depending on the cell areas of an associated Laguerre (i.e. a weighted Voronoi) tessellation. We consider the high number of cell limit of such systems and, using a modulated energy argument, we prove convergence towards smooth solutions of nonlinear diffusion PDEs of porous medium type. |
| title | Gradient flows of interacting Laguerre cells as discrete porous media flows |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2304.05069 |