Slowing Allee effect versus accelerating heavy tails in monostable reaction diffusion equations
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Publication:2965350
DOI10.1088/1361-6544/AA53B9zbMATH Open1358.35056arXiv1505.04626OpenAlexW2964184992MaRDI QIDQ2965350
Author name not available (Why is that?)
Publication date: 2 March 2017
Published in: (Search for Journal in Brave)
Abstract: We focus on the spreading properties of solutions of monostable reaction-diffusion equations. Initial data are assumed to have heavy tails, which tends to accelerate the invasion phenomenon. On the other hand, the nonlinearity involves a weak Allee effect, which tends to slow down the process. We study the balance between the two effects. For algebraic tails, we prove the exact separation between "no acceleration and acceleration". This implies in particular that, for tails exponentially unbounded but lighter than algebraic , acceleration never occurs in presence of an Allee effect. This is in sharp contrast with the KPP situation [19]. When algebraic tails lead to acceleration despite the Allee effect, we also give an accurate estimate of the position of the level sets.
Full work available at URL: https://arxiv.org/abs/1505.04626
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