Document Type
Article
Publication Title
Nonlinear Analysis
Abstract
We investigate the existence of traveling wave solutions for the reaction–diffusion equation ∂u(x,t)∂t=Δu(x,t−τ1)+f(u(x,t),u(x,t−τ2)), where τ1, τ2 > 0. This model is motivated by ecological applications in which migration rates incorporate historical effects and reproduction/death processes are subject to time delays at a given location. To address such systems under standard monotonicity assumptions, we extend the classical monotone iteration method. A key step involves a thorough investigation of the Green function associated with the functional equation x″(t)−ax′(t+r)−bx(t+r)=f(t), where a ≠ 0 and b > 0. Building on the resulting framework, we construct quasi-upper and lower solutions for the Belousov–Zhabotinski equations, thereby demonstrating the existence of traveling waves when delays are sufficiently small.
Department
Mathematics and Statistics
Publication Date
4-2026
Recommended Citation
Barker, W., & Nguyen, M. (2026). Traveling waves in reaction-diffusion equations with delay in the diffusion term. Nonlinear Analysis, 271, Article 114125.https://doi.org/10.1016/j.na.2026.114125
