Exact Boundary Value Controllability of a Class of Hyperbolic Equations

Abstract

Let $c(t)$ be a real-valued function which is analytic for $t \geqq 0$ and $\Omega $ be a bounded, open set in $R^n $ with smooth boundary. Sufficient conditions are given which insure that control processes modeled by partial differential equations of the form \[\frac{{\partial ^2 u}}{{\partial t^2 }} - \sum\limits_{i = 1}^n {\frac{{\partial ^2 u}}{{\partial x_i^2 }}} + c(t)u = 0\] in the cylinder $\Omega \times [ {0,\infty } )$ are exactly controllable in any finite time T which exceeds the diameter of $\Omega $ by control forces applied on the wall of the cylinder.