An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems
Analysis of PDEs
2017-04-18 v1
Abstract
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.
Cite
@article{arxiv.1704.04541,
title = {An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems},
author = {Thomas Gallouët and Maxime Laborde and Léonard Monsaingeon},
journal= {arXiv preprint arXiv:1704.04541},
year = {2017}
}