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Traveling fronts for a delayed reaction–diffusion system with a quiescent stage

✍ Scribed by Shi-Liang Wu; Hai-Qin Zhao

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
289 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

In this paper, we study the traveling wave fronts of a delayed reaction-diffusion system with a quiescent stage for a single species population with two separate mobile and stationary states. By transforming the corresponding wave system into a scalar delayed differential equation with an integral term, we establish the existence of the minimal wave speed c min , and the asymptotic behavior, monotonicity and uniqueness (up to a translation) of the traveling wave fronts. In particular, the effects of the delay and transfer rates on the minimal wave speed are studied.

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✍ Hai-Qin Zhao 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 256 KB

This paper is concerned with a reaction-diffusion system with spatio-temporal delay. Under the bistable assumptions, the existence of traveling wavefronts is established by transforming the system with spatio-temporal delay to a three-dimensional reactiondiffusion system without delay. The uniquenes