A smoothing property of a hyperbolic system and boundary controllability Control of partial differential equations

We investigate a method with which one can deduce controllability results from smoothing properties. Previous applications of the method were for partial di®er-ential equations like the Euler-Bernoulli Beam Equation (Petrowski-Hyperbolic). In this paper we study the method's applicability to a strictly hyperbolic system by considering the boundary controllability of a vibrating Timoshenko beam with physical characteristics that may vary along the length of the beam. Two cases are considered: A beam which is clamped at one end, the other end being controlled by a torque and transverse force; and a beam which is hinged at one end, where a control torque is applied, and free at the other end, where a control force is applied. 1 Introduction. In this paper, we study the boundary controllability of a Timoshenko beam. The main purpose of the paper is to try out a recent method of controllability (see below) on a strictly hyperbolic system. Previously, the method had been applied to the Euler-Bernoulli beam equation and the SchrÄodinger equation