Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients

M. M. Cavalcanti

Address. Departamento de Matematica - Universidade Estadual de Maringa, 87020-900 Maringa - PR, BRAZIL.


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.