Advanced Mathematical Models & Applications

The classical solvable of a nonlinear inverse boundary value problem for linearized equation of longitudinal waves in rods with periodic and integral condition is investigated. To investigate the solvable of the stated problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. We then use the Fourier method to reduce such an equivalent problem to a system of integral equations. Furthermore, we prove the existence and uniqueness theorem for the auxiliary problem by the contraction mappings principle. Based on the equivalency of these problems, the existence and uniqueness theorem for the classical solution of the original inverse problem is proved.