On a curvature flow model for embryonic epidermal wound healing. (English) Zbl 1429.53075
Summary: The paper is a mathematical investigation of a curvature flow model for embryonic epidermal wound healing proposed by A. Ravasio et al. [“Gap geometry dictates epithelial closure efficiency”, Nature Commun. 6, Article No. 7683, 13 p. (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.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53E99 | Geometric evolution equations |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
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