The leading edge of a free boundary interacting with a line of fast diusion
The leading edge of a free boundary interacting with a line of fast diusion
复制标题
自由边界的前缘与快速扩散线相互作用
DOI：
10.1090/spmj/1658
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
J. Roquejoffre
中科院分区：
文献类型：
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作者：
L. Caffarelli;J. Roquejoffre
这项工作的目标是解释一个系统解的扩展水平集的一个意想不到的特征，其中发生反应扩散现象的半平面与自身具有较大扩散的线交换质量。该系统由 H. Berestycki、L. Rossi 和第二作者 [4] 提出，作为通过快速扩散线增强生物入侵的模型。通过 A.-C 进行数值观察。 Coulon [7] 认为，正面的前缘不是位于线上，而是位于下半平面。我们解释了与进行模拟的系统密切相关的自由边界问题的这种行为。我们针对这个问题构造了行波，分析了行波线附近的自由边界，并证明它具有数值模拟预测的行为。
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-diusion phenomena take place, exchanges mass with a line having a large diusion of its own. The system was proposed by H. Berestycki, L. Rossi and the second author [4] as a model of enhancement of biological invasions by a line of fast diusion. It was observed numerically by A.-C. Coulon [7] that the leading edge of the front, rather than being located on the line, was in the lower half plane. We explain this behaviour for a free boundary problem much related to the system for which the simulations were made. We construct travelling waves for this problem, analyse their free boundary near the line, and prove that it has the behaviour predicted by the numerical simulations.