Controllability of a One-Dimensional Dynamic Debonding Model
Abstract
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 \( C1 \) regularity settings, and construct exact controls toward these target states.
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