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Accepted for publication in Appl. Math. Res. ExpressInternational audienceWe prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a sequence of continuations which leads to further insight into the system. In particular, the transition occurs through a singular perturbation which seems new in this context, connecting the system with a Wentzell type boundary value problem

Existence of Travelling Waves for a Reaction–Diffusion System with a Line of Fast Diffusion