Abstract
In this paper, a reaction-diffusion equation with discrete time delay that describes the dynamics of the blood cell production is analyzed. The existence of the traveling wave front solutions is demonstrated using the technique of upper and lower solutions and the associated monotone iteration.
Highlights
It is well know that the traveling wave theory was initiated in 1937 by Kolmogorov, Petrovskii, Piskunov [1] and Fisher [2]
Gomez and Trofimchuk [5] considered the Fisher-KPP equation and their results showed that each monotone traveling wave could be found via an iteration procedure by using the special montone integral operators
Li and Zhou [14] derived a sufficient and necessary condition that guarantees the existence of positive periodic solutions of Equation (1.2) with periodic coefficients
Summary
It is well know that the traveling wave theory was initiated in 1937 by Kolmogorov, Petrovskii, Piskunov [1] and Fisher [2]. The theory of traveling wave solutions to reaction-diffusion equations is one of the fast developing areas of modern mathematics and has attracted much attention due to its significance in biology, chemistry, epidemiology and physics, see [3] [4] and the reference cited therein. The traveling wave problem for reaction-diffusion systems with delay has been widely studied.
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