Equation of flexural vibration with an unknowns coefficients

In this work, we study one inverse boundary value problem for the equations of flexural vibrations of a bar.The essence of the problem is that it is required together with the solution to determine the unknown coefficient.The problem is considered in a rectangular area.To solve the considered problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out.The existence and uniqueness of a solution to the auxiliary problem are proved with the help of contracted mappings.Then the transition to the original inverse problem is made, as a result, a conclusion is made about the solvability of the original inverse problem.