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.

翻译：我们研究了一类离散模型，其中一组粒子随时间演化，遵循依赖于关联拉盖尔（即加权Voronoi）剖分中细胞面积的能量的梯度流。我们考虑了此类系统在细胞数量趋于无穷时的极限，并利用调制能量论证，证明了其收敛于多孔介质型非线性扩散偏微分方程的光滑解。