Existence, uniqueness, and continuous dependence of the solution to a hyperbolic equation with an unknown coefficient

In this paper, we study the existence, uniqueness, and continuous dependence of the solution for a hyperbolic equation arising in the framework of inverse problems. To achieve this, we first prove the existence and uniqueness of the solution to the associated direct problem using the energy inequality method. Then, by means of fixed point theory, we establish the existence and uniqueness of the solution to the inverse problem.