On a class of population dynamics problem with mixed boundary conditions
The paper deals with a linear model describing the dynamics of a single species population with age dependence and spatial structure. The equation is considered in a bounded domain in \({\mathbb R}^n\), having a regular boundary. The birth process is described by a nonlocal term and the diffusion of individuals in the domain follows a Fick's law. The main result of the paper concerns the null controllability for the model. The exact null controllability is proven by employing a Carleman inequality with mixed boundary conditions for the backward adjoint population dynamics problem. The proof of this estimate is obtained using a standard technique from the theory of abstract parabolic equations. It is shown that one can expect to compute the initial distribution of individuals using observations on a small part of the boundary.
scientific article; zbMATH DE number 5822860