Address. Departamento de Matematica - Universidade Estadual de Maringa, 87020-900 Maringa - PR, BRAZIL.
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Abstract. In this paper we study the boundary exact controllability for the equation $$ \frac{\partial}{\partial t}\left(\alpha (t){{\partial y}\over { \partial t}}\right)-\sum_{j=1}^n{{\partial}\over {\partial x_j}}\left (\beta (t)a(x){{\partial y}\over {\partial x_j}}\right)=0\;\;\;\hbox{in}\;\; \Omega\times (0,T)\,, $$ when the control action is of Dirichlet-Neumann form and $\Omega$ is a bounded domain in ${\bold R}^n$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.
AMSclassification. 35B40, 35B35, 35L99.
Keywords. Wave equation, boundary value problem, exact controllability, Dirichlet-Neumann condition.