Control and stabilization results for strongly coupled degenerate/singular hyperbolic systems

In this paper, we consider a system of two degenerate and singular wave equations coupled through velocities, where only one of the equations is controlled or damped. Under some technical assumptions on the coefficients of the system, we prove new controllability and stability results. First, we derive the explicit time for the indirect controllability of the corresponding control problem. Second, we prove that the total energy of the associated stabilization problem is exponentially decaying to zero, providing an explicit formula for the decay rate. The proofs of our results are mainly based on careful energy estimates and suitable Hardy-Poincaré type inequalities.