  This paper deals with some control problems related to structured population
dynamics with diffusion. Firstly, we investigate the regional control for an
optimal harvesting problem (the control acts in a subregion $\omega$ of the
whole domain $\Omega$). Using the necessary optimality conditions, for a fixed
$\omega$, we get the structure of the harvesting effort which gives the maximum
harvest; with this optimal effort we investigate the best choice of the
subregion $\omega$ in order to maximize the harvest. We introduce an iterative
numerical method to increase the total harvest at each iteration by changing
the subregion where the effort acts. Numerical tests are used to illustrate the
effectiveness of the theoretical results. We also consider the problem of
eradication of an age-structured pest population dynamics with diffusion and
logistic term, which is a zero-stabilization problem with constraints. We
derive a necessary condition and a sufficient condition for
zero-stabilizability. We formulate a related optimal control problem which
takes into account the cost of intervention in the subregion $\omega$.
