Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability

We consider a Timoshenko beam involving potentials and Dirichlet-Neumann boundary conditions. We prove new Carleman estimates with boundary and interior observations for this system. We achieve this by constructing appropriate weight functions accounting for the presence of Neumann boundary conditions. As an application, we derive exact boundary and internal controllability results for this system.