Travelling waves of the diffusive Nicholson’s blowflies equation with strong generic delay kernel and non-local effect

• Published in: Nonlinear analysis Vol. 68; no. 5; pp. 1263 - 1270
• Main Authors: Zhang, Jianming, Peng, Yahong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.03.2008; Elsevier
• Subjects: Exact sciences and technology; Mathematical analysis; Mathematics; Nicholson’s blowflies; Non-local effect; Sciences and techniques of general use; Travelling waves; Non-local effect; Travelling waves; 92D25; 35K57; Nicholson’s blowflies; Travelling waves; Nicholson's blowflies; Non-local effect; Mathematical model; Travelling wave; 35K57; 92D25; Delay equation; Nonlinear analysis
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2006.12.019

In this paper, we consider travelling wave solutions for the diffusive Nicholson’s blowflies equation incorporating time delay and diffusion. Special attention is paid to the modelling of the time delay to incorporate associated non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times. For the strong generic delay kernel, we show that travelling wave solutions exist provided that the delay is sufficiently small, using the geometric singular perturbation theory.