Existence and uniqueness of a solution for a BVP from developmental biology

Research output: Contribution to journalArticle

Abstract

Recently, Sherrat [J. Appl. Math. 47, 147 (1991)] introduced a model for the behaviour of an epithelial sheet after a section of the sheet had been removed. Consideration of radially symmetric equilibria reduces the original PDE to an ODE boundary value problem. Sherratt employed formal perturbation analyses to produce an expansion for the solution by exploiting a small parameter ε. In this article the author gives a rigorous proof that, for each ε >0, a solution exists and that it is unique. This is achieved using a topological shooting argument. Also given are results concerning the physically relevant 'sharp edge' of the solution near the boundary.

Original languageEnglish (US)
Pages (from-to)239-249
Number of pages11
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume51
Issue number3
DOIs
StatePublished - Dec 1 1993

All Science Journal Classification (ASJC) codes

  • Molecular Biology
  • Statistics and Probability
  • Computational Mathematics
  • Development
  • Management, Monitoring, Policy and Law
  • Demography
  • Applied Mathematics
  • Mathematics(all)

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