On the propagation speed of the single monostable equation

TL;DR

This paper investigates the propagation speed in monostable reaction-diffusion equations, establishing conditions based on decay rates of traveling waves, with implications for broader dynamical systems including nonlocal diffusion.

Contribution

It introduces a new criterion for propagation speed based on decay rates, applicable to general monostable systems using the comparison principle.

Findings

Derived a necessary and sufficient condition for speed selection.

Extended the analysis to nonlocal diffusion equations.

Provided insights into the decay behavior of minimal traveling waves.

Abstract

In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition that reveals the essence of propagation phenomena. Moreover, since our argument relies solely on the comparison principle, it can be extended to more general monostable dynamical systems, such as nonlocal diffusion equations.