A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

Carlier, Guillaume; Laborde, Maxime

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