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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.
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Chen et al. (2000) studied this question.
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