Geodesic
The leading edge of a free boundary interacting with a line of fast diffusion
Algebra i analiz, Tome 32 (2020) no. 3, pp. 149-179.

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The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half-plane in which reaction-diffusion phenomena take place exchanges mass with a line having a large diffusion of its own. The system was proposed by H. Berestycki, L. Rossi and the second author as a model of enhancement of biological invasions by a line of fast diffusion. It was observed numerically by A.-C. Coulon that the leading edge of the front, rather than being located on the line, was in the lower half-plane. We explain this behavior for a closely related free boundary problem. We construct travelling waves for this problem, and the analysis of their free boundary near the line confirms the predictions of the numerical simulations.
Keywords: expanding level sets, reaction-diffusion phenomena, line of fast diffusion. 
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L. A. Caffarelli; J.-M. Roquejoffre. The leading edge of a free boundary interacting with a line of fast diffusion. Algebra i analiz, Tome 32 (2020) no. 3, pp. 149-179. http://geodesic.mathdoc.fr/item/AA_2020_32_3_a6/

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