Open AccessTraveling wave solutions of periodic nonlocal Fisher-KPP equations with non-compact asymmetric kernel
Author(s) -
Aijun Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022061
Subject(s) - eigenvalues and eigenvectors , kernel (algebra) , traveling wave , mathematical analysis , multivibrator , mathematics , physics , pure mathematics , quantum mechanics , voltage
This paper deals with front propagation for nonlocal monostable equations in spatially periodic habitats. In the authors' earlier works, assuming the existence of principal eigenvalue, it is shown that there are periodic traveling wave solutions to a spatially periodic nonlocal monostable equation with symmetric and compact kernel connecting its unique positive stationary solution and the trivial solution in every direction with all propagating speeds greater than the spreading speed in that direction. In this paper, first assuming the existence of principal eigenvalue, we extend the results to the case that the kernel is asymmetric and supported on a non-compact region. In addition, without the assumption of the existence of principal eigenvalue, we explore the existence of semicontinuous traveling wave solutions.