Paper's Title:

Existence and Approximation of Traveling Wavefronts for the Diffusive Mackey-Glass Equation

Author(s):

C. Ramirez-Carrasco and J. Molina-Garay

Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
E-mail: carloshrc1989@gmail.com
 molina@imca.edu.pe

Abstract:

In this paper, we consider the diffusive Mackey-Glass model with discrete delay. This equation describes the dynamics of the blood cell production. We investigate the existence of traveling wavefronts solutions connecting the two steady states of the model. We develop an alternative proof of the existence of such solutions and we also demonstrate the existence of traveling wavefronts moving at minimum speed. The proposed approach is based on the use technique of upper-lower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.

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