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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.

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
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