Volume 2, Number 4, Fall 1994
A SINGULAR PERTURBATION THEOREM
FOR EVOLUTION EQUATIONS AND
TIMESCALE 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 timescale argument is justified
for agestructured 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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