Journal of Dynamics and Differential Equations

, Volume 19, Issue 2, pp 391–436

Existence, Uniqueness and Asymptotic Stability of Traveling Wavefronts in A Non-Local Delayed Diffusion Equation

Article

DOI: 10.1007/s10884-006-9065-7

Cite this article as:
MA, S. & WU, J. J Dyn Diff Equat (2007) 19: 391. doi:10.1007/s10884-006-9065-7

In this paper, we study the existence, uniqueness, and global asymptotic stability of traveling wave fronts in a non-local reaction–diffusion model for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. Under realistic assumptions on the birth function, we construct various pairs of super and sub solutions and utilize the comparison and squeezing technique to prove that the equation has exactly one non-decreasing traveling wavefront (up to a translation) which is monotonically increasing and globally asymptotic stable with phase shift.

Keywords

Non-local reaction-diffusion equation traveling wave front existence uniqueness asymptotic stability comparison principle 

AMS (1991) Subject Classification

34K30 35B40 35R10 58D25 

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.School of Mathematical SciencesNankai UniversityTianjinPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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