Inrecentyears,populationgrowthmodelswithspatialdiffusionhavebeenextensivelystudiedbymanyauthors(forexample,see[1-5]).Inthispaper,apopulationgrowthmodelisconsideredwithadiscreteage-dependenceandspatialdiffusion,andisinvestigatedinasemigroupframework.Thespectralpropertiesofthepopulationoper-atoraregiven.Onthebasisofsuchspectralconsideration,theasymptoticbehaviourofthesemigroupgeneratedbythepopulationoperatorisobtained.Finally,anonlinearpopulationgrowthmodelisconsideredanditsstabilityisanalyzed.
