Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 136, Issue -, Pages 92-157Publisher
ELSEVIER
DOI: 10.1016/j.matpur.2020.02.002
Keywords
Reaction-diffusion equations; Transition fronts; Propagation speed; Exterior domains; Domains with branches
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Funding
- Excellence Initiative of Aix-Marseille University-A*MIDEX, a French Investissements d'Avenir programme
- European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) ERC Grant [321186]
- ANR NONLOCAL project [ANR-14-CE25-0013]
- China Scholarship Council
- NSF of China [11401134, 11971128]
- postdoctoral scientific research development fund of Heilongjiang Province [LBH-Q17061]
- Agence Nationale de la Recherche (ANR) [ANR-14-CE25-0013] Funding Source: Agence Nationale de la Recherche (ANR)
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This paper is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior domains we show that all transition fronts propagate with the same global mean speed, which turns out to be equal to the uniquely defined planar speed. In domains with multiple cylindrical branches, we show that the solutions emanating from some branches and propagating completely are transition fronts propagating with the unique planar speed. We also give some geometrical and scaling conditions on the domain, either exterior or with multiple cylindrical branches, which guarantee that any transition front has a global mean speed. (C) 2020 Elsevier Masson SAS. All rights reserved.
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