| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1601 - 1625 | |
| DOI | https://doi.org/10.1051/m2an/2025021 | |
| Published online | 18 June 2025 | |
Gradient flows of interacting laguerre cells as discrete porous media flows
Inria, Université de Lille, Inria, CNRS, UMR 8524 – Laboratoire Paul Painlevé, 59000 Lille, France
* Corresponding author: andrea.natale@inria.fr
Received:
24
July
2024
Accepted:
24
March
2025
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.
Mathematics Subject Classification: 35A15 / 49S05 / 49Q22 / 65M75
Key words: Porous media equations / Lagrangian discretizations / semi-discrete optimal transport
© The authors. Published by EDP Sciences, SMAI 2025
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