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A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

Carlier, Guillaume; Laborde, Maxime (2016), A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts, Nonlinear Analysis. Theory, Methods & Applications, 150, p. 1-18. 10.1016/j.na.2016.10.026

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01332356
Date
2016-06
Journal name
Nonlinear Analysis. Theory, Methods & Applications
Volume
150
Publisher
Pergamon Press
Pages
1-18
Publication identifier
10.1016/j.na.2016.10.026
Metadata
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laborde, Maxime
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a splitting scheme. The splitting scheme combines transport steps by the divergence-free part of the drift and semi-implicit minimization steps à la Jordan-Kinderlherer Otto to deal with the potential part.
Subjects / Keywords
Helmholtz decomposition; nonlin-ear diffusions; splitting; nonlocal drift; Wasserstein gradient flows; Jordan-Kinderlehrer-Otto scheme

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