An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems

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.
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Submitted on : Friday, April 14, 2017 - 10:26:29 PM
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Thomas Gallouët, Maxime Laborde, Leonard Monsaingeon. An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, In press, ⟨10.1051/cocv/2018001⟩. ⟨hal-01508911⟩

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