Volume 25, 2019
|Number of page(s)||32|
|Published online||05 April 2019|
An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
Mathematics Department, Université de Liége,
2 INRIA Paris MOKAPLAN, Paris, France.
3 McGill University, Montreal, Canada.
4 IECL Université de Lorraine, Nancy, France.
5 GFM Universidade de Lisboa, Lisboa, Portugal.
* Corresponding author: firstname.lastname@example.org
Accepted: 21 December 2017
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.
Mathematics Subject Classification: 35K15 / 35K57 / 35K65 / 47J30
Key words: Unbalanced optimal transport / Wasserstein-Fisher-Rao / Hellinger-Kantorovich / JKO scheme / reaction-diffusion-advection equations
© EDP Sciences, SMAI 2019
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