A reaction-diffusion model for a single species with age structure. I: Travelling wavefronts on unbounded domains. (English) Zbl 0999.92029

Summary: We derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. We show that if the mature death and diffusion rates are age independent, then the total mature population is governed by a reaction-diffusion equation with time delays and non-local effects. We also consider the existence, uniqueness and positivity of solutions to the initial-value problem for this type of equations.
Moreover, we establish the existence of a travelling-wave front for the special case when the birth function is the one which appears in the well-known Nicholson’s blowflies equation and we consider the dependence of the minimal wave speed on the mobility of the immature population.


92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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