Gradient flows of interacting Laguerre cells as discrete porous media flows

Publication date: 11 April 2023

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.

Has companion code repository: https://github.com/andnatale/gradient_flows_of_interacting_cells

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