Gradient flows of interacting Laguerre cells as discrete porous media flows

04/11/2023

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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.

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Gradient flows of interacting Laguerre cells as discrete porous media flows

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Gradient flows of interacting Laguerre cells as discrete porous media flows

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