simultaneous control of the source terms in a vibrational string problem

in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functional and the lipschitzcontinuity of the gradient are investigated. minimizing sequence is obtained by the method of the projectionof the gradient.