Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations

TL;DR

This paper investigates the existence and stability of traveling wave solutions in spatially periodic nonlocal monostable equations, extending understanding of wave propagation in heterogeneous environments with nonlocal dispersal.

Contribution

It demonstrates the existence of unique stable periodic traveling waves connecting stationary and trivial solutions under certain conditions, for all speeds above the spreading speed.

Findings

Existence of stable periodic traveling waves in specific conditions

Traveling waves exist for all speeds greater than the spreading speed

Unique stable solutions connect stationary and trivial states

Abstract

This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal dispersal has a unique spatially periodic positive stationary solution and has a spreading speed in every direction. In this paper, we show that a spatially periodic nonlocal monostable equation with certain spatial homogeneity or small nonlocal dispersal distance has a unique stable periodic traveling wave solutions connecting its unique spatially periodic positive stationary solution and the trivial solution in every direction for all speeds greater than the spreading speed in that direction.