| Summary: | 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≥0,0<x<π,w(t,x)=∫τAlu(t,a,x)da,t≥t0≥Al>0,0<x<π,τ≥0,u(t,0,x)=f(w(t,x)),t≥t0≥Al>0,0<x<π,ux(t,a,0)=ux(t,a,π)=0,t≥t0≥Al>0,a≥0, $$ \textstyle\begin{cases} \frac{\partial u}{\partial t}+\frac{\partial u}{\partial a}=D(a)\frac{ \partial^{2}{u}}{\partial x^{2}}-d(a)u, & t\geq t_{0}\geq A_{l}>0, a \geq 0, 0< x< \pi , \\ w(t,x)= \int_{\tau }^{A_{l}}u(t,a,x)\,da,& t\geq t_{0}\geq A_{l}>0, 0< x< \pi ,\tau \geq 0, \\ u(t,0,x)=f(w(t,x)), & t\geq t_{0}\geq A_{l}>0, 0< x< \pi ,\\ u_{x}(t,a,0)=u_{x}(t,a,\pi )=0, & t\geq t_{0}\geq A_{l}>0, a \geq 0, \end{cases} $$ 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.
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