A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

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• 作者：Guillaume Carlier ; ^{carlier@ceremade.dauphine.fr} ; Maxime Laborde ^{laborde@ceremade.dauphine.fr}
• 关键词：35K15 ; 35K40
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：150
• 期：Complete
• 页码：1-18
• 全文大小：676 K
• 卷排序：150

文摘

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.