On the Semigroup for Age Dependent Population Dynamics with Spatial Diffusion

We continue a population model with age dependence and spatial diffusion in the semigroup framework, in which the assumptions of our previous paper [Manuscripta Math.66 (1990), 161-180] that birth and death rates are independent of spatial variables are removed. The infinitesimal generator is identified and its spectrum studied, and accordingly, by using a positive semigroup theory, we determine its dominant eigenvalue and hence the asymptotic expression is obtained.