On systems of continuity equations with nonlinear diffusion and nonlocal drifts

2015/05/06 by Guillaume Carlier, Carlier, Guillaume, Maxime Laborde +1
Mathematics · #35K15 #35K40 #49J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K15 #msc:35K40 #msc:49J40

paper · pdf · doi:10.48550/arxiv.1505.01304

arxiv created 2015/05/06 · arxiv updated 2015/05/07

Abstract

This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a gradient (in the physical space), we obtain existence by a semi-implicit Jordan-Kinderlehrer-Otto scheme. Then, in the nonpotential case, we derive existence from a regularization procedure and parabolic energy estimates. We also address the uniqueness issue by a displacement convexity argument.

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