Carleman Estimates and Controllability for a Degenerate Structured Population Model

Abstract

In this paper we study the null controllability property for a single population model in which the population y depends on time t, space x, age a and size $$\tau $$. Moreover, the diffusion coefficient k is degenerate at a point of the domain or both extremal points. Our technique is essentially based on Carleman estimates. The $$\tau $$ dependence requires us to modify the weight for the Carleman estimates, and accordingly the proof of the observability inequality. Thanks to this observability inequality we obtain a null controllability result for an intermediate problem and finally for the initial system through suitable cut off functions.