Farkas JZ (2003) On the asymptotic behaviour of the non-autonomous Gurtin-MacCamy equation. Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, 46, pp. 111-120. http://www.cs.elte.hu/~annalesm/vol46trt.pdf
In this paper we consider a non-autonomous age-structured population dynamical model. Our model is a generalization of the classical Gurtin-MacCamy system, that is we consider explicitly time dependent vital rates, which makes a problem a non-autonomus one. Similarly to Iannelli, M. etal (2002), we investigate the global behaviour of the solutions of the system. Motivated by the stability conditions arrived in Farkas, J.Z., forthcoming, for the similar autonomous model, we are able to show - under not only mathematically simple even biologically meaningful conditions - some results for the asymptotics of the solutions.
Structured population dynamics; boundedness of solutions
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica: Volume 46