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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.