Traveling Wave Solutions of Spatially Periodic Nonlocal Monostable Equations

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.

30 pages

References in corpus (4)

• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
• Nonlocal anisotropic dispersal with monostable nonlinearity
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
• Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds

Cited by in corpus (13)

• Traveling waves and spreading speeds for time-space periodic monotone systems
• On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications
• Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity
• Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity
• Positive Stationary Solutions and Spreading Speeds of KPP Equations in Locally Spatially Inhomogeneous Media
• Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable media
• Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media
• Regularity of transition fronts in nonlocal dispersal evolution equations
• Propagation Phenomena for A Reaction-Advection-Diffusion Competition Model in A Periodic Habitat
• Notes on nonlocal dispersal equations in a periodic habitat
• Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media
• Spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media
• Approximations of Random Dispersal Operators/Equations by Nonlocal Dispersal Operators/Equations