Acceleration in integro-differential combustion equations

TL;DR

This paper investigates acceleration phenomena in monostable integro-differential equations with ignition nonlinearity, covering fractional Laplace operators and convolutions, by constructing a sub-solution to understand the dynamics of acceleration.

Contribution

It introduces a unified approach to study acceleration in integro-differential equations, including fractional Laplace operators and convolutions, through the construction of a key sub-solution.

Findings

Demonstrates acceleration phenomena in various integro-differential equations

Provides a unified framework for fractional Laplace and convolution operators

Highlights the flattening effect in accelerated propagation

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.