Traveling wavefronts in a reaction–diffusion model with chemotaxis and nonlocal delay effect. (February 2019)

• Record Type: Journal Article
• Authors: Li, Dong; Guo, Shangjiang
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 736
• Page End: 754
• Publication Date: 2019-02
• Subjects: Reaction–diffusion model -- Chemotaxis -- Nonlocal delay effect -- Traveling wavefront -- Perturbation method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.08.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is devoted to the study of traveling wavefronts of large wave speed for a reaction–diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method. The proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain Banach space, coupled with the Fredholm theory and the Banach contraction mapping principle. This result is illustrated by an application to the chemotaxis–diffusion–growth model with the logistic source and a single delay effect.