Abstract
In this paper, we investigate the controllability for the one-dimensional plate equation in intervals with a moving boundary. This equation models the vertical displacement of a point x at time t in a bar with uniform cross section. We assume the ends of the bar with small and uniform variations. More precisely, we have introduced functions α(t) and β(t) modeling the motion of these ends. We present the following results: the existence and uniqueness of Nash equilibrium, the approximate controllability with respect to the leader control, and the optimality system for the leader control.
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