Displacement convexity for the entropy in semidiscrete nonlinear\n Fokker-Planck equations

2016/11/15 by José A. Carrillo, Ansgar Jüngel, Carrillo, José A. +3 · 1 citation
Mathematics · Physics and Astronomy · #53C21 #60J27 #65M20 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #Applied mathematics #Balanced flow #Convexity #Entropy (arrow of time) #FOS: Mathematics #Finite difference #Fokker–Planck equation #Functional Analysis (math.FA) #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematics #Nonlinear system #Partial differential equation #Physics #Quantum mechanics #Statistical Mechanics and Entropy #math.AP #math.FA #msc:53C21 #msc:60J27 #msc:65M20

paper · pdf · doi:10.48550/arxiv.1611.04716

published in arXiv (Cornell University) (Cornell University)

arxiv created 2016/11/15 · openalex publication_date 2016/11/15 · arxiv updated 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The displacement \λ-convexity of a nonstandard entropy with respect to\na nonlocal transportation metric in finite state spaces is shown using a\ngradient flow approach. The constant \λ is computed explicitly in terms\nof a priori estimates of the solution to a finite-difference approximation of a\nnonlinear Fokker-Planck equation. The key idea is to employ a new mean\nfunction, which defines the Onsager operator in the gradient flow formulation.\n

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