Electron. J. Differential Equations, Vol. 2019 (2019), No. 51, pp. 1-21.

Monotone iteration scheme and its application to partial differential equation systems with mixed nonlocal and degenerate diffusions

Qiuling Huang, Xiaojie Hou

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
Xiaojie Hou
Department of Mathematics and Statistics
University of North Carolina Wilmington
NC 28403, USA
email: houx@uncw.edu

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