Exact Controllability of Hybrid System of Elasticity with Locally Distributed Control in Non-cylindrical Domain

Hybrid system of elasticity in domains with moving boundary is discussed. This equation characterizes the motion of a beam with a fixed endpoint and the other moving one. By using the multiplier method to estimate the energy function, We determine the observability of dual systems. Therefore, the original system is exact controllable, when the speed of the moving endpoint is less than some constant.