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

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.

Keywords

• Nonlocal diffusion
• traveling wave solution
• asymptotics
• Schauder fixed point theorem
• upper and lower solutions
• uniqueness