One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

Authors:
Martial Agueh;Malcolm Bowles
Affiliations:
Department of Mathematics and Statistics, University of Victoria, Victoria, Canada V8W 3R4;Department of Mathematics and Statistics, University of Victoria, Victoria, Canada V8W 3R4
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2013

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Abstract

We numerically approximate, on the real line, solutions to a large class of parabolic partial differential equations which are "gradient flows" of some energy functionals with respect to the L p -Wasserstein metrics for all p1. Our method relies on variational principles involving the optimal transport problem with general strictly convex cost functions.