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Алгебра и анализ, 2020, том 32, выпуск 3, страницы 149–179
(Mi aa1703)
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Статьи
The leading edge of a free boundary interacting with a line of fast diffusion
L. A. Caffarellia, J.-M. Roquejoffreb a The University of Texas at Austin, Mathematics Department RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas 78712-1202, U.S.A.
b Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse III, 118 route de Narbonne, 31062 Toulouse cedex, France
Аннотация:
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.
Ключевые слова:
expanding level sets, reaction-diffusion phenomena, line of fast diffusion.
Поступила в редакцию: 29.07.2019
Образец цитирования:
L. A. Caffarelli, J.-M. Roquejoffre, “The leading edge of a free boundary interacting with a line of fast diffusion”, Алгебра и анализ, 32:3 (2020), 149–179; St. Petersburg Math. J., 32:3 (2021), 499–522
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1703 https://www.mathnet.ru/rus/aa/v32/i3/p149
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