An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems

Hellinger-Kantorovich; JKO scheme; Reaction-diffusion-advection equations; Unbalanced optimal transport; Wasserstein-Fisher-Rao; Advection; Diffusion in liquids; Optimal transport; Reaction diffusion; Computational fluid dynamics

Abstract :

[en] In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric setting. We use a constructive method, alternating minimizing movements for the Wasserstein distance and for the Fisher-Rao distance, and prove existence of weak solutions for general scalar reaction-diffusion-advection equations. We extend the approach to systems of multiple interacting species, and also consider an application to a very degenerate diffusion problem involving a Gamma-limit. Moreover, some numerical simulations are included. © EDP Sciences, SMAI 2019.

Disciplines :

Mathematics

Author, co-author :

Gallouët, Thomas ; Université de Liège - ULg

Laborde, M.; McGill University, Montreal, Canada

Monsaingeon, L.; IECL Université de Lorraine, Nancy, France, GFM Universidade de Lisboa, Lisboa, Portugal

Language :

English

Title :

An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems

Publication date :

2019

Journal title :

ESAIM: Control, Optimisation and Calculus of Variations

ISSN :

1292-8119

eISSN :

1262-3377

Publisher :

EDP Sciences, France

Volume :

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

Institut national de la recherche scientifique
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 13 November 2021

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