A JKO SPLITTING SCHEME FOR KANTOROVICH-FISHER-RAO GRADIENT FLOWS - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Mathematical Analysis Year : 2017

A JKO SPLITTING SCHEME FOR KANTOROVICH-FISHER-RAO GRADIENT FLOWS

(1) , (2, 3)
1
2
3

Abstract

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric , recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case of internal energies. The interest is double: On the one hand we prove existence of weak solutions for a certain class of reaction-advection-diffusion equations, and on the other hand this process is constructive and well adapted to available numerical solvers.
Fichier principal
Vignette du fichier
GM_final.pdf (615.51 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01273849 , version 1 (14-02-2016)
hal-01273849 , version 2 (05-01-2022)

Identifiers

  • HAL Id : hal-01273849 , version 2

Cite

Thomas Gallouët, Leonard Monsaingeon. A JKO SPLITTING SCHEME FOR KANTOROVICH-FISHER-RAO GRADIENT FLOWS. SIAM Journal on Mathematical Analysis, 2017, 49(2). ⟨hal-01273849v2⟩
372 View
230 Download

Share

Gmail Facebook Twitter LinkedIn More