Abstract
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.
Funder
Agence Nationale de la Recherche
Fonds De La Recherche Scientifique - FNRS
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Reference47 articles.
1. Quasi-static evolution and congested crowd transport
2. Ambrosio L., Fusco N. and Pallara D., Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000).
3. Ambrosio L., Gigli N. and Savaré G., Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel (2005).
4. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
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