In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-dependence and spatial diffusion, and isinvestigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviourof the semigroup generated by the population operator is obtained. Finally, a nonlinearpopulation growth model is considered and its stability is analyzed.
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