Controlabilidade Exata e Aproximada da Equação da Onda Linear

Abstract
We studied exact (boundary and internal) and approximate (boundary and internal)
controllability for the system associated to linear wave equation with Dirichlet boundary
condition. For this purpose, we carry out a detailed analysis on existence, uniqueness
and regularity of the solution for the system. To study exact controllability, we use
the Hilbert Uniqueness Method (HUM). Through variational methods we show how the
exact controllability can be reduced to a minimization problem. For the approximate
controllability, we study a minimization problem via the duality method in the sense of
Fenchel, where we find, in a natural way, a functional which give us control of the minimum
norm.
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