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Sharp exponent of acceleration in general nonlocal equations with a weak Allee effect

Abstract : We study a acceleration phenomenon arising in monostable integro-differential equations with a weak Allee effect. Previous works have shown its occurrence and have given correct upper bounds on the rate of expansion, but precise lower bounds were still missing. In this paper, we provide a sharp lower bound of acceleration for a large class of dispersion operators. Our results cover fractional Laplace operators and standard convolutions in a unified way. To achieve this, we construct a refined sub-solution that captures the expected dynamics of the accelerating solution. We also take advantage of a general flattening estimate for the solution, that we prove along the way and is of independent interest.
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https://hal.archives-ouvertes.fr/hal-03452141
Contributor : Guillaume Legendre Connect in order to contact the contributor
Submitted on : Tuesday, July 19, 2022 - 9:33:56 AM
Last modification on : Tuesday, September 13, 2022 - 2:14:33 PM

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  • HAL Id : hal-03452141, version 2
  • ARXIV : 2105.09911

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Emeric Bouin, Jérôme Coville, Guillaume Legendre. Sharp exponent of acceleration in general nonlocal equations with a weak Allee effect. 2022. ⟨hal-03452141v2⟩

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