Singular Perturbation Theorem for Evolution Equations and Time-Scale Argumentsfor Structured Population Models

摘要

A generalization of a particular case of Tikhonov's singular perturbation theoremto Banach spaces is presented. From this, sufficient conditions under which a faithful simplification by a time scale argument is justified for age structured population models is obtained. An explicit formulation of the approximating, ordinary differential equation, model is obtained. The precise class of structured population models for which similar results hold is described. It is concluded that from a biological and mathematical point of view the aim is to attempt to extend Tikhonov's result to some of the operators considered.