A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts. (February 2017)

• Record Type: Journal Article
• Authors: Carlier, Guillaume; Laborde, Maxime
• Is Part Of: Nonlinear analysis. Volume 150(2017)
• Page Start: 1
• Page End: 18
• Publication Date: 2017-02
• Subjects: 35K15 -- 35K40; Wasserstein gradient flows -- Jordan–Kinderlehrer–Otto scheme -- Splitting -- Nonlocal drift -- Nonlinear diffusions -- Helmholtz decomposition; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.026
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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–Kinderlehrer Otto to deal with the potential part.