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

So, Joseph W.-H.; Wu, Jianhong; Zou, Xingfu

Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2012, 1841-1853 (2001).

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.

MSC:

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

Keywords:

Cauchy problem; diffusion; structured population; travelling waves; time delays; non-local effects