Null Controllability of Size-Age Dependent Population Dynamics Models

Abstract

This article examines an infinite-dimensional linear control system that describes population models structured by age, size, and spatial position. The control is localized with respect to space, age and size; an estimate of the time required to bring the system to zero is provided. We demonstrate the null controllability of the model using a technique that avoids the explicit use of parabolic Carleman estimates. Instead, this method combines the observability estimates of the final state with the use of characteristics and estimates of the associated semigroup. Furthermore, we extend this work by highlighting the difference in controllability time for two models with different birth kernels.