Qiuling Huang, Xiaojie Hou
Abstract:
A monotone iteration scheme for traveling waves based on ordered upper
and lower solutions is derived for a class of nonlocal dispersal system
with delay. Such system can be used to study the competition among
nonlocally diffusive species and degenerately diffusive species.
An example of such system is studied in detail. We show the existence
of the traveling wave solutions for this system by this iteration scheme.
In addition, we study the minimal wave speed, uniqueness, strict
monotonicity and asymptotic behavior of the traveling wave solutions.
Submitted May 6, 2018. Published April 18, 2019.
Math Subject Classifications: 35C07, 35B40.
Key Words: Nonlocal diffusion; traveling wave solution; asymptotics;
Schauder fixed point theorem; upper and lower solutions; uniqueness.
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Qiuling Huang School of Mathematics and Quantitative Economics Shandong University of Finance and Economics Jinan, 250014, China email: hql_shj@163.com |
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Xiaojie Hou Department of Mathematics and Statistics University of North Carolina Wilmington NC 28403, USA email: houx@uncw.edu |
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