ESAIM. Control, optimisation and calculus of variations, 2019, Vol.25 (8), p.8
2019
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Details
- Autor(en) / Beteiligte
- Titel
- An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
- Ist Teil von
- ESAIM. Control, optimisation and calculus of variations, 2019, Vol.25 (8), p.8
- Ort / Verlag
- Les Ulis: EDP Sciences
- Erscheinungsjahr
- 2019
- Quelle
- EZB Electronic Journals Library
- Beschreibungen/Notizen
- 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.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 1292-8119, 1262-3377eISSN: 1262-3377DOI: 10.1051/cocv/2018001Titel-ID: cdi_hal_primary_oai_HAL_hal_01508911v1
- Format
- –
- Schlagworte
- 35K15, 35K57, 35K65, 47J30, Advection, Advection-diffusion equation, Analysis of PDEs, Computational fluid dynamics, Computer simulation, Diffusion, Diffusion in liquids, Hellinger-Kantorovich, JKO scheme, Mathematics, Mathématiques, Optimal transport, Physical, chemical, mathematical & earth Sciences, Physique, chimie, mathématiques & sciences de la terre, Reaction diffusion, Reaction-diffusion-advection equations, Unbalance, Unbalanced optimal transport, Wasserstein-Fisher-Rao