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On the diffusive Nicholson’s blowflies equation with nonlocal delay. (English) Zbl 1134.35064
Summary: This paper is concerned with the diffusive Nicholson’s blowflies model with nonlocal (or spatiotemporal) delay. When the spatial variable is one-dimensional, we establish the existence of travelling wave-front solutions by using the approach developed by Z.-C. Wang, W.-T. Li, and S. Ruan [J. Differ. Equations 222, No. 1, 185–232 (2006; Zbl 1100.35050)] on the existence of travelling front solutions of reaction-diffusion systems with nonlocal delay. Moreover, we consider the dependence of the minimal wave speed on the delay and the mobility of the population. Our main finding here is that delay can induce slow travelling wave-fronts and the mobility of the population can increase fast travelling wave-fronts. In particular, if we choose some special kernel forms, then our results include and improve some known results.

MSC:
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
35R10 Functional partial differential equations
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