Optimal Positional Control Of One-Dimensional Wave Equation

This paper is concerned with the existence and uniqueness of the optimal positional control for a one-dimensional wave equation with first boundary value and a positional parameter in right side. Firstly, the existence and uniqueness of a weak solution of the wave equation with first boundary value in general case are proved by using the Galerkin method. Secondly, the existence of optimal positional control for given cost functional is proved, and a example shows that the uniqueness of optimal positional control may be not held. Thirdly, for a special case.the estimates of uh, ut.h are established by using the solution of adjoint equation, and a necessary condition satisfied by the optimal positional control is given. Finally, a special example is studied.