Approximation of the Semigroup of a Linear Age-Dependent Population Model with Spatial Diffusion

Abstract

. In this paper a variational version of the Trotter-Kato theorem is applied to an infinitesimal generator A of a C 0 -semigroup in a Hilbert space that is assumed to be the sum of two linear operators A and B defined on the intersection of their domains, where A \Gamma !I is m-dissipative for some ! ? 0 and B is the generator of an analytic semigroup associated with a bounded V -coercive sesquilinear form. An approximation of the semigroup generated by A is obtained from given approximations of the sesquilinear forms appertaining to A and B. This result is applied to the semigroup generated by an age-dependent population model with spatial diffusion, and numerical examples are presented to demonstrate feasibility of the scheme. Research in part supported by FWF through Spezialforschungsbereich F 003 Optimierung und Kontrolle. Running head: Age-dependent population diffusion Mail proofs to: Waltraud Huyer Institut fur Mathematik Universitat Wien Strudlhofgasse 4 A-1090 Vienna Aus..