Convergence of a particle method for diffusive gradient flows in one dimension

Interactions between Partial Differential Equations & Functional Inequalities

29 September 17:00 - 17:30

Francesco Saverio Patacchini - Imperial College London

We approximate diffusive gradient flows with finite numbers of particles in one dimension. As the quadratic Wasserstein energy is not defined for point-masses, we spread uniformly the mass of each particle in some interval around it. This "tessellation" gives a discrete energy defined on point-masses, which Gamma-converges in the Wasserstein topology to its continuum version as the number of particles increases. Using an abstract result for the convergence of gradient flows in metric spaces by S. Serfaty, we show the convergence of the resulting discrete gradient flow to the continuum one. This is joint work with J. A. Carrillo, Y. Huang, P. Sternberg and G. Wolansky.
José A. Carrillo
Imperial College London
Ivan Gentil
Institut Camille Jordan
Helge Holden
NTNU - Norwegian University of Science and Technology
Cédric Villani
Institut Henri Poincaré (IHP)
Boguslaw Zegarlinski
Imperial College London


José A. Carrillo


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