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The shape of a free boundary driven by a line of fast diffusion

We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free boundary is asymptotic to a line at infinity, whose angle to the horizontal is dicatated by the velocity of the wave imposed by the line. This helps understanding some rather counter-intuitive numerical simulations of [8].

preprint2020arXivOpen access
Luis CaffarelliJean-Michel Roquejoffre
math.AP
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Luis CaffarelliJean-Michel Roquejoffre

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