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In this paper, a nonlinear inverse boundary value problem for thesecond-order hyperbolic equation with nonlocal conditions is studied. Toinvestigate the solvability of the original problem, we first consider anauxiliary inverse boundary value problem and prove its equivalence (in acertain sense) to the original problem. Then using the Fourier method andcontraction map pings principle, the existence and uniqueness theorem forauxiliary problem is proved. Further, on the basis of the equivalency of theseproblems the existence and uniqueness theorem for the classical solution of theconsidered inverse coefficient problem is proved for the smaller value of time.

Nonlinear inverse problem for identifying a coefficient of the lowest term in hyperbolic equation with nonlocal conditions