Mustafa Kemal University, Faculty of Science and Literature, Department of Mathematics, Hatay, Turkey
Ataturk University, Faculty of Science, Department of Mathematics, 25240, Erzurum, Turkey
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 state
the generalized (weak) solution about the considered problem. The existence and uniqueness of the solution
for optimal control problem is investigated. The Frechet derivative of the functional and the Lipschitz
continuity of the gradient are investigated. Minimizing sequence is obtained by the method of the projection
of the gradient.