A semigroup approach to age-dependent population dynamics with time delay

Abstract

We study the McKendrick type models of population dynamics with instantaneous time delay in the birth rate. The models involve first order partial differential equations with nonlocal and delayed boundary conditions. We show that a semigroup can be associated to it and identify the infinistimal generator. Its spectral properties are analyzed yielding large time behaviour. An interesting result is that if the total population converges to an equilibrium it will converge to it in an oscillatory fashion. Further, we consider a logistic ara age-dependent model with delay. A nonlinear semigroup is constructed to describe the evolution of the population. Existence and uniqueness of the nonlinear equation are proved.