Some remarks on the asymptotic behavior of the semigroup associated with age-structured diffusive populations (Q1955632)

This paper deals with a class of linear population models incorporating age and spatial structure. Assuming that the spatial structure of individuals is described by a diffusion term, an abstract functional analytic formulation of the model is provided, which is based on the property of maximal regularity of the diffusion operator. Using technical tools from \(C_0\)-semigroup theory, an analysis of the asymptotic time behaviour of solutions can be carried out. The main results of the work consist of describing the infinitesimal generator of the \(C_0\)-semigroup associated to the solutions of the abstract formulation of the model. An analysis of its spectral properties provides a precise description of the stability of the trivial solution as well as results on the asynchronous exponential growth property.