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

. 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..

Well-Posedness Of A Linear Age-Dependent Population Model With Spatial Diffusion In L²

. A linear model for an age-structured population with random diffusion in a bounded domain \Omega ae R n is studied in the semigroup framework in L 2 . Three different approaches to establishing wellposedness of the problem are presented. Two of them involve applying known results on the m-dissipativeness of the sum of two m-dissipative operators to the population operator and the diffusion operator. Key words. Linear age-dependent population dynamics with spatial diffusion, C 0 -semigroups, sum of two m-dissipative operators, evolution systems. 1. Introduction Mathematical models for age-structured populations with spatial diffusion were proposed by Gurtin (1973). Many authors have dealt with linear and nonlinear problems of this kind since then (cf. the bibliography Huyer (1992)). In this paper we consider a linear model for an age-structured population with random diffusion in a bounded domain\Omega ae R n . Let u(t; a; x) be the population density at time t 0, where a ..

On Periodic Cohort Solutions of a Size-Structured Population Model

. We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable `substrate'. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter fi. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n 2) with small size differences will tend to a periodic one-cohort solution as t !1. Key words: Size-structured populations -- Discontinuous reproduction -- Variable environment -- Periodic cohort solutions -- Stability 1. Introduction Reproduction is an event in the life of individuals. When there is quite some variation in the individual states at which such events occur, a formal appeal to the law of large numbers allows one to model reproduction by rates at the population level. When reproduction occurs upon reaching a specified individual state, one can still work wi..

Global optimization by multilevel coordinate search

Abstract. Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results