Optimal control problem for the coefficient function in a hyperbolic partial differential equation

In this thesis, considering optimal control theory, theoretical stages related to the controllability of the coefficient function taken place in a hyperbolic problem has been dealt with. In the first chapter, it has been given fundamental information about the optimal control problems and hyperbolic equations. In the second chapter, definitons of some mathematical concepts mentioned in this thesis have been given. In the next chapter, existence and uniqueness of the generalized solution for hyperbolic problem considered has been obtained. However, it has been demonstrated that the optimal solution for optimal control problem is exist and unique. In the following chapters, adjoint problem which is necessary for gradient of the cost functional and second adjoint problem has been acquired. Also, necessary condition for optimal solution has been presented. Finally, it has been refer from how minimizing sequence converges to optimal solution is found.