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.
Domains
Analysis of PDEs [math.AP]
Fichier principal
Gallouet_Laborde_Monsaingeon_2017.pdf (3.14 Mo)
Télécharger le fichier
a-prey_predator-jkofr-00.pdf (139.08 Ko)
Télécharger le fichier
a-prey_predator-jkofr-100.pdf (107.9 Ko)
Télécharger le fichier
a-prey_predator-jkofr-15.pdf (81.1 Ko)
Télécharger le fichier
a-prey_predator-jkofr-35.pdf (62.31 Ko)
Télécharger le fichier
a-prey_predator-jkofr-50.pdf (49.97 Ko)
Télécharger le fichier
a-prey_predator-jkofr-65.pdf (67.18 Ko)
Télécharger le fichier
a-prey_predator-jkofr-85.pdf (121.8 Ko)
Télécharger le fichier
b-prey_predator-jkofr-00.pdf (138.31 Ko)
Télécharger le fichier
b-prey_predator-jkofr-100.pdf (113.09 Ko)
Télécharger le fichier
b-prey_predator-jkofr-15.pdf (75.25 Ko)
Télécharger le fichier
b-prey_predator-jkofr-35.pdf (82.99 Ko)
Télécharger le fichier
b-prey_predator-jkofr-50.pdf (79.83 Ko)
Télécharger le fichier
b-prey_predator-jkofr-65.pdf (67.91 Ko)
Télécharger le fichier
b-prey_predator-jkofr-85.pdf (92.9 Ko)
Télécharger le fichier
c-prey_predator-jkofr-00.pdf (188.66 Ko)
Télécharger le fichier
c-prey_predator-jkofr-100.pdf (141.51 Ko)
Télécharger le fichier
c-prey_predator-jkofr-15.pdf (106.92 Ko)
Télécharger le fichier
c-prey_predator-jkofr-35.pdf (79.83 Ko)
Télécharger le fichier
c-prey_predator-jkofr-50.pdf (89.01 Ko)
Télécharger le fichier
c-prey_predator-jkofr-65.pdf (90.84 Ko)
Télécharger le fichier
c-prey_predator-jkofr-85.pdf (136.99 Ko)
Télécharger le fichier
dens-jkoCFL-100.pdf (127.08 Ko)
Télécharger le fichier
dens-jkoCFL-140.pdf (127.11 Ko)
Télécharger le fichier
dens-jkoCFL-200.pdf (138.31 Ko)
Télécharger le fichier
dens-jkoCFL-60.pdf (130.94 Ko)
Télécharger le fichier
dens-jkofr100-00-eps-converted-to.pdf (102.9 Ko)
Télécharger le fichier
masse.pdf (18.24 Ko)
Télécharger le fichier
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|
Origin | Files produced by the author(s) |
---|