Global attractivity in a non-monotone age-structured model with age-dependent diffusion and death rates

Abstract

Abstract In this paper, the global attractivity of the homogeneous equilibrium solution for the diffusive age-structured model {∂u∂t+∂u∂a=D(a)∂2u∂x2−d(a)u,t≥t0≥Al>0,a≥0,00,00,00,a≥0, $$ \textstyle\begin{cases} \frac{\partial u}{\partial t}+\frac{\partial u}{\partial a}=D(a)\frac{ \partial^{2}{u}}{\partial x^{2}}-d(a)u, & t\geq t_{0}\geq A_{l}>0, a \geq 0, 00, 00, 00, a \geq 0, \end{cases} $$ is established when the diffusion and death rates, D(a) $D(a)$ and d(a) $d(a)$, respectively, are age dependent during the whole life of the species, and when the birth function f(w) $f(w)$ is nonmonotone. In the paper, we also present some demonstrative examples.

Keywords

• Homogeneous equilibrium solution
• Global attractivity
• Age-structured model
• Non-monotone birth function
• Age-dependent death rate
• Age-dependent diffusion rate