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**Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects.**
*(English)*
Zbl 1017.92024

Summary: 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 effects 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.

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.

### MSC:

92D25 | Population dynamics (general) |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35K55 | Nonlinear parabolic equations |

65N06 | Finite difference methods for boundary value problems involving PDEs |