Null controllability of a retarded population dynamics model with interior degeneracy

In this work, we establish a null controllability property of a dispersive age-structured population dynamics model with finite-time delay on the mortality rate term. We assume that the dispersion term includes an interior degeneracy satisfying some suitable assumptions. To achieve our main results, we act according to the classical procedure, which is the Carleman estimates of a suitable adjoint system, and then its associated observability inequality. It is well known that the basis of Carleman's estimates is an adjusted weight function and one of the originalities of our article is the expression of the function as a function of age and time variables.