On some non linear evolution systems which are perturbations of Wasserstein gradient flows

2015/05/30 by Maxime Laborde, Laborde, Maxime
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #Applied mathematics #Bounded function #Class (philosophy) #Computer science #Convexity #Dermatological and Skeletal Disorders #Displacement (psychology) #Domain (mathematical analysis) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Space (punctuation) #Uniqueness #math.AP

paper · pdf · doi:10.48550/arxiv.1506.00126

published in arXiv (Cornell University) (Cornell University)

arxiv created 2015/05/30 · openalex publication_date 2015/05/30 · arxiv updated 2015/06/02 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28

Abstract

This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here we extend results known in the periodic case to the whole space and on a smooth bounded domain. Existence is obtained using a semi-implicit Jordan-Kinderlehrer-Otto scheme and uniqueness follows from a displacement convexity argument.

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