Special Session 99: Emerging Trends in Analysis and Control of PDEs

Controllability of a one-dimensional debonding model
Nicola De Nitti
University of Pisa
Italy
Co-Author(s):    N. De Nitti, A. Shao
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 $C^1$ regularity settings, and construct exact controls toward these target states.