Boundary Value Control of a Class of Hyperbolic Equations in a General Region

Abstract

Let $c(t)$ be a real valued function which is analytic for $t \geqq 0$ and which is such that, for some positive integer $N \geqq 3$, the operator \[L_N = \sum_{i = 1}^N {\frac{{\partial ^2 }}{{\partial x_i^2 }} - \frac{{\partial ^2 }}{{\partial t^2 }}} - c(t)\] satisfies Huygens’ principle in the sense of Hadamard’s “minor premise”. Let $\Omega $ be a smooth, bounded domain in $R^n $, $n \geqq 2$. We show that control processes which are modeled by an equation $L_n u = 0$ in the cylindrical region $\Omega \times [0,\infty )$ are exactly controllable in any finite time T which exceeds the diameter of $\Omega $ by control forces applied on the wall of the cylinder.