Dissipation for a non-convex gradient flow problem of a Patlack–Keller–Segel type for densities on Rd, d≥3. (July 2021)

• Record Type: Journal Article
• Authors: Carlen, Eric A.; Ulusoy, Suleyman
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: primary 35K65 35B45 35J20; Degenerate parabolic equation -- Energy functional -- Gradient flow -- Free-energy solutions -- Blow-up -- Global existence; 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.2021.112314
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study an evolution equation that is the gradient flow in the 2-Wasserstein metric of a non-convex functional for densities in R d with d ≥ 3 . Like the Patlack–Keller–Segel system on R 2, this evolution equation features a competition between the dispersive effects of diffusion, and the accretive effects of a concentrating drift. We determine a parameter range in which the diffusion dominates, and all mass leaves any fixed compact subset of R d at an explicit polynomial rate.