A Free Boundary Problem Arising in a Model of Wound Healing

In this paper we consider a system of two semilinear parabolic reaction-diffusion equations with a free boundary, which arises in a model of corneal epithelial wound healing. We prove that the initial-boundary value problem has a unique solution and that complete healing is achieved in finite time. We then proceed to consider travelling wave solutions of the same system and establish the existence of such a solution.