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Strong ergodicity for perturbed dual semigroups and application to age- dependent population dynamics. (English) Zbl 0761.92028
An age-dependent population model described by a Lotka-McKendric-Von Foerster system is studied using the perturbation theory of dual semigroups in a sun-reflexive Banach space. A brief summary of the results for dual semigroups theory and perturbation theory of dual semigroups in a sun-reflexive Banach space is given. Also asymptotic properties of the evolutionary system generated by a Lipschitz continuous perturbation of a ${C}_{0}$-semigroup are given. The concept of strong ergodicity for the evolutionary system is introduced and this concept is applied to Lotka’s renewal equation to prove strong ergodicity of the age structured population model with time dependent vital rates. The controllability of a demographic model is also studied by using the total fertility rate as a control.
##### MSC:
 92D25 Population dynamics (general) 47D06 One-parameter semigroups and linear evolution equations 93B05 Controllability 45K05 Integro-partial differential equations