On a curvature flow model for embryonic epidermal wound healing. (December 2019)

• Record Type: Journal Article
• Authors: He, Shuhui; Wheeler, Glen; Wheeler, Valentina-Mira
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 53C44 -- 58J35; Curve shortening flow -- Free boundary conditions -- Biological membranes -- Geometric analysis; 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.2019.111581
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper is a mathematical investigation of a curvature flow model for embryonic epidermal wound healing proposed by Ravasio et al. (2015). Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a round point in finite time. We also study the singularity, showing that the singularity profile after continuous rescaling is that of a circle. One of the key new results we require is a maximal time estimate, which is also of independent interest.