Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion
We consider here a model of accelerating fronts, consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proposed in a previous work by H. Berestycki, L. Rossi and the a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-10-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/10.3934/mine.2021006/fulltext.html |
| _version_ | 1819291311639887872 |
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| author | Anne-Charline Chalmin Jean-Michel Roquejoffre |
| author_facet | Anne-Charline Chalmin Jean-Michel Roquejoffre |
| author_sort | Anne-Charline Chalmin |
| collection | DOAJ |
| description | We consider here a model of accelerating fronts, consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proposed in a previous work by H. Berestycki, L. Rossi and the authors, as a mechanism of front acceleration by a line of fast diffusion. In this latter work, it was indeed proved that the propagation in the direction of the line was exponentially fast in time. Inspired by numerical simulations of the first author, we make the estimate more precise by computing a time algebraic correction. |
| first_indexed | 2024-12-24T03:36:37Z |
| format | Article |
| id | doaj.art-6e0fcf49cb0a44b9907acbced30fe138 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-24T03:36:37Z |
| publishDate | 2021-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-6e0fcf49cb0a44b9907acbced30fe1382022-12-21T17:17:02ZengAIMS PressMathematics in Engineering2640-35012021-10-013111610.3934/mine.2021006Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusionAnne-Charline Chalmin0Jean-Michel Roquejoffre1Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse III, 118 route de Narbonne, 31062 Toulouse cedex, FranceInstitut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse III, 118 route de Narbonne, 31062 Toulouse cedex, FranceWe consider here a model of accelerating fronts, consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper half-plane. It was proposed in a previous work by H. Berestycki, L. Rossi and the authors, as a mechanism of front acceleration by a line of fast diffusion. In this latter work, it was indeed proved that the propagation in the direction of the line was exponentially fast in time. Inspired by numerical simulations of the first author, we make the estimate more precise by computing a time algebraic correction.https://www.aimspress.com/article/10.3934/mine.2021006/fulltext.htmlfisher-kppfront propagationline of nonlocal diffusion |
| spellingShingle | Anne-Charline Chalmin Jean-Michel Roquejoffre Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion Mathematics in Engineering fisher-kpp front propagation line of nonlocal diffusion |
| title | Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion |
| title_full | Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion |
| title_fullStr | Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion |
| title_full_unstemmed | Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion |
| title_short | Improved bounds for reaction-diffusion propagation driven by a line of nonlocal diffusion |
| title_sort | improved bounds for reaction diffusion propagation driven by a line of nonlocal diffusion |
| topic | fisher-kpp front propagation line of nonlocal diffusion |
| url | https://www.aimspress.com/article/10.3934/mine.2021006/fulltext.html |
| work_keys_str_mv | AT annecharlinechalmin improvedboundsforreactiondiffusionpropagationdrivenbyalineofnonlocaldiffusion AT jeanmichelroquejoffre improvedboundsforreactiondiffusionpropagationdrivenbyalineofnonlocaldiffusion |