Exact controllability in the interior for a strongly coupled elastic system

In this work, we studied the exact controllability of a strongly coupled elastic system. First, we studied the case of a system where potential terms are absent. Next, we present the system's observability inequality including the potential terms. To prove the inequality of observability for the system without the potential, we used the multipliers technique and explained the control time and its relation with the coefficients of the system. Then, we apply Hilbert uniqueness method to prove the exact controllability. To prove the observability inequality of system with potential, we use a technique based on perturbation of the solution and the observability inequality for the system without the potential.