Sharp exponent of acceleration in integro-differential equations with weak Allee effect.

We study acceleration phenomena in monostable integro-differential equations with weak Allee effect. Previous works have shown its occurrence and obtained correct upper bounds on the rate of expansion, but precise lower bounds were left open. In this paper, we provide a sharp lower bound of acceleration for a large class of dispersion operators. Indeed, our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper. To achieve this, we construct a refined sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty.