Carleman estimates and null controllability for a degenerate population model

TL;DR

This paper establishes Carleman estimates and null controllability results for a degenerate population model, addressing boundary and interior degeneracies to control population dynamics effectively.

Contribution

It introduces new Carleman estimates for degenerate PDEs and demonstrates null controllability for models with interior or boundary degeneracy.

Findings

Carleman estimates for degenerate PDEs established

Null controllability achieved with interior control

Control functions localized within the spatial domain

Abstract

We deal with a degenerate model describing the dynamics of a population depending on time, on age and on space. We assume that the degeneracy can occur at the boundary or in the interior of the space domain and we focus on null controllability problem. To this aim, we prove first Carleman estimates for the associated adjoint problem, then, via cut off functions, we prove the existence of a null control function localized in the interior of the space domain.