On the Solvability of an Inverse Boundary Value Problem for a Second‐Order Hyperbolic Equation With a Memory Term

ABSTRACT In this paper, we consider an inverse boundary value problem for a hyperbolic equation with a memory term, subject to a nonlocal boundary condition. The primary objective is to determine the unknown coefficient and to solve the problem of interest. First, we introduce a definition of a classical solution, followed by the proof of existence and uniqueness for the direct problem. The original problem is then reduced to an equivalent formulation. We employ the method of separation of variables to transform the non‐self‐adjoint problem into a system of integral equations. The existence and uniqueness of the solution to this integral equation are established via the contraction mapping principle. Finally, we demonstrate the existence and uniqueness of the classical solution to the inverse problem, subject to an additional nonlocal condition.