Null Controllability of Size-Age Dependent Population Dynamics Models

TL;DR

This paper proves the null controllability of a complex population dynamics model structured by age, size, and space, using a novel approach that avoids traditional Carleman estimates, and compares controllability times for different birth kernels.

Contribution

It introduces a new method for establishing null controllability in infinite-dimensional population models without relying on Carleman estimates.

Findings

The model is null controllable within a finite time.

Controllability time varies with different birth kernels.

A new technique combines observability and characteristics for control analysis.

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.