Abstract:Our goal in 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 occur 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.

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中文翻译：

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自由边界的前沿与快速扩散线相互作用

摘要：我们在这项工作中的目标是解释系统解的扩展能级集的意外特征，在该系统中，发生反应扩散现象的半平面与自身扩散较大的线交换质量。该系统由H. Berestycki，L。Rossi和第二作者提出，作为通过快速扩散线增强生物入侵的模型。由A.-C进行数值观察。Coulon认为前部的前缘位于下半平面，而不是位于直线上。我们为一个密切相关的自由边界问题解释了这种行为。我们针对此问题构造行波，对行附近的自由边界的分析证实了数值模拟的预测。

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