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On a curvature flow model for embryonic epidermal wound healing

Journal Article


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.

Publication Date


  • 2019

Citation


  • He, S., Wheeler, G. & Wheeler, V. (2019). On a curvature flow model for embryonic epidermal wound healing. Nonlinear Analysis Theory Methods and Applications, 189 111581-1-111581-41.

Scopus Eid


  • 2-s2.0-85073705630

Start Page


  • 111581-1

End Page


  • 111581-41

Volume


  • 189

Place Of Publication


  • United Kingdom

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.

Publication Date


  • 2019

Citation


  • He, S., Wheeler, G. & Wheeler, V. (2019). On a curvature flow model for embryonic epidermal wound healing. Nonlinear Analysis Theory Methods and Applications, 189 111581-1-111581-41.

Scopus Eid


  • 2-s2.0-85073705630

Start Page


  • 111581-1

End Page


  • 111581-41

Volume


  • 189

Place Of Publication


  • United Kingdom