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Volume 2,     Number 4,     Fall 1994

 

A SINGULAR PERTURBATION THEOREM
FOR EVOLUTION EQUATIONS AND
TIME-SCALE ARGUMENTS FOR
STRUCTURED POPULATION MODELS
G. GREINER, J.A.P. HEESTERBEEK, J.A.J. METZ

Abstract. In this paper we present a generalization of a finite dimensional singular perturbation theorem to Banach spaces. From this we obtain sufficient conditions under which a faithful simplification by a time-scale argument is justified for age-structured models of slowly growing populations. An explicit formulation for the approximating, ordinary differential equation, model is obtained. Finally, we describe the precise class of structured population models for which we conjecture that a similar result holds.

 

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