On a nonconservative huyperbolic system describing the nonlinear age dependent populations growth

Abstract

This paper addresses the issue of an existence theory for a system of hyperbolic partial differential equations arising in age dependent population dymanics. The abstract model incorporates both the traditional ecological models (e.g. predator-prey and competition) and the epidemics models. In order to include the latter situation the theory has been developed for non-diagonal systems. Global existence has been investigated and sufficient conditions for the continuation of the solutions are provided.