Null controllability for a degenerate population equation with memory

TL;DR

This paper establishes null controllability for a degenerate population model with a memory term, using new Carleman estimates to handle the added complexity introduced by the memory effect.

Contribution

It introduces the first analysis of null controllability for a population equation with degeneracy and memory, developing novel Carleman estimates for the adjoint problem.

Findings

Null controllability achieved under specific kernel conditions.

New Carleman estimates developed for degenerate equations with memory.

The approach extends controllability results to more complex population models.

Abstract

In this paper we consider the null controllability for a population model depending on time, on space and on age. Moreover, the diffusion coefficient degenerate at the boundary of the space domain. The novelty of this paper is that for the first time we consider the presence of a memory term, which makes the computations more difficult. However, under a suitable condition on the kernel we deduce a null controllability result for the original problem via new Carleman estimates for the adjoint problem associated to a suitable nonhomogeneous parabolic equation.