Controllability of a One-Dimensional Dynamic Debonding Model

We investigate a one-dimensional dynamic debonding model, introduced by Freund (1990), in which the wave equation is coupled with a Griffith criterion governing the propagation of the fracture. In particular, we study the boundary controllability of the system to a prescribed target state. Our main results provide precise characterizations of the reachable target states, in both $C^{ 0, 1 }$ and $C^1$ regularity settings, and construct exact controls toward these target states.