Acceleration in integro-differential combustion equations

Abstract

We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. 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 sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty. This study involves the flattening effect occurring in accelerated propagation phenomena.

Version 0. Changes to come. arXiv admin note: substantial text overlap with arXiv:2105.09911