Gradient flows of interacting Laguerre cells as discrete porous media flows
Numerical Analysis
2025-04-01 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2304.05069,
title = {Gradient flows of interacting Laguerre cells as discrete porous media flows},
author = {Andrea Natale},
journal= {arXiv preprint arXiv:2304.05069},
year = {2025}
}