Internal Stabilizability of Some Diffusive Models

We consider a single species population dynamics model with age dependence, spatial structure, and a nonlocal birth process arising as a boundary condition. We prove that under a suitable internal feedback control, one can improve the stabilizability results given in Kubo and Langlais [J. Math. Biol. 29 (1991), 363–378]. This result is optimal. Our proof relies on an identical stabilizability result of independent interest for the heat equation, that we state and prove in Section 3.