Slowing Allee effect versus accelerating heavy tails in monostable reaction diffusion equations

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 st...

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Bibliographic Details
Published inNonlinearity Vol. 30; no. 2; pp. 687 - 702
Main Author Alfaro, Matthieu
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.02.2017
Subjects
acceleration
Allee effect
Analysis of PDEs
heavy tails
Mathematics
reaction diffusion equations
spreading properties
spreading properties
heavy tails
92D25
Allee effect
reaction diffusion equations
35B40
acceleration AMS Subject Classifications: 35K57
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Summary: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 the presence of an Allee effect. This is in sharp contrast with the KPP situation [20]. When algebraic tails lead to acceleration despite the Allee effect, we also give an accurate estimate of the position of the level sets.
Bibliography:London Mathematical Society
NON-100937.R1
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa53b9