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

Gallouët, Thomas; Laborde, Maxime; Monsaingeon, Léonard (2019), An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems, ESAIM: Control, Optimisation and Calculus of Variations, p. 27. 10.1051/cocv/2018001

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Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01508911
Date
2019
Journal name
ESAIM: Control, Optimisation and Calculus of Variations
Pages
27
Publication identifier
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Author(s)
Gallouët, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laborde, Maxime
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Monsaingeon, Léonard
Institut Élie Cartan de Lorraine [IECL]
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 framework. 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.
Subjects / Keywords
Wasserstein distance; Fisher-Rao distance