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In this paper we consider a degenerate population equation in divergence form depending on time, on age and on space and we prove a related null controllability result via Carleman estimates.

We establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by previous contributions for degeneracy and singularity on the boundary. In addition, we consider non-smooth coefficients, thus preventing the use of standard calculations in this framework.

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on Carleman estimates for the associated adjoint problem. The novelty of interior degeneracy does not let us adapt previous Carleman estimates to our situation. As an application, observability inequalities are established.

We consider a parabolic problem with degeneracy in the interior of the spatial domain and we focus on the well-posedness of the problem and on inverse source problems. The novelties of the present paper are two. First, the degeneracy point is in the interior of the spatial domain. Second, we consider Neumann boundary conditions so that no previous result can be adapted to this situation. [ABSTRACT FROM AUTHOR]