EXISTENCE AND UNIQUENESS OF A SOLUTION FOR A BVP FROM DEVELOPMENTAL BIOLOGY

Recently, Sherrat [J. Appl. Math. 47, 147 (1991)] introduced a model f or the behaviour of an epithelial sheet after a section of the sheet h ad been removed. Consideration of radially symmetric equilibria reduce s 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 epsilon. In this article the author g ives a rigorous proof that, for each epsilon > 0, a solution exists an d that it is unique. This is achieved using a topological shooting arg ument. Also given are results concerning the physically relevant 'shar p edge' of the solution near the boundary.