Exact controllability of the wave equation in a thin domain with a wave-like boundary (Q2706898)

The exact controllability of a wave equation in a thin domain with waved boundary and its asymptotic behavior, when the depth tends to zero, is studied. Using the J. J. Lious method the author proves the control existence and regularity and some of the normal derived increasing (direct and reverse) inequalities which give estimations for homogeneous and retrograde solutions. It is proved that the exact control limit is the control problem for which the associate operator is a wave function.NEWLINENEWLINENEWLINEThe paper spreads the results obtained by \textit{J. Saint Jean Paulin} and \textit{M. Vanninatan} [Port. Math. 51, 421-453 (1994; Zbl 0805.73065)] in the cylindrical model.