Journal of Nonlinear Science

, Volume 13, Issue 3, pp 289–310

Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Nonlocal Delayed Effects


DOI: 10.1007/s00332-003-0524-6

Cite this article as:
Liang & Wu J. Nonlinear Sci. (2003) 13: 289. doi:10.1007/s00332-003-0524-6


In this paper, we consider the growth dynamics of a single-species population with two age classes and a fixed maturation period living in a spatial transport field. A Reaction Advection Diffusion Equation (RADE) model with time delay and nonlocal effect is derived if the mature death and diffusion rates are age independent. We discuss the existence of travelling waves for the delay model with three birth functions which appeared in the well-known Nicholson's blowflies equation, and we consider and analyze numerical solutions of the travelling wavefronts from the wave equations for the problems with nonlocal temporally delayed effects. In particular, we report our numerical observations about the change of the monotonicity and the possible occurrence of multihump waves. The stability of the travelling wavefront is numerically considered by computing the full time-dependent partial differential equations with nonlocal delay.

Key words. Travelling wave, reaction advection diffusion equation, structured population, nonlocal time delay, existence, numerical approximation AMS Classification. 92D25, 35K55, 65M06, 35N06

Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  • Liang
    • 1
  • Wu
    • 1
  1. 1.Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada e-mail:, wujh@mathstat.yorku.caCA