  In this paper, motivated by a physics problem, we investigate some numerical
and computational aspects for the problem of hierarchical controllability in a
one-dimensional wave equation in domains with a moving boundary. Some controls
act in part of the boundary and define a strategy of equilibrium between them,
considering a leader control and a follower. Thus, we introduced the concept of
hierarchical control to solve the problem and mapped the Stackelberg Strategy
between these controls. A total discretization of the problem is presented for
a numerical evaluation in spaces of finite dimension, an algorithm for
evaluation of the problem is presented as the combination of finite element
method (FEM) and finite difference method (FDM). The algorithm efficiency and
computational results are illustrated for some experiments using the softwares
Freefem++ and MatLab.

Optimization and Control;Analysis of PDEs