A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition

摘要

This article is concerned with the study of the unique solvability of a timenonlocal inverse boundary value problem for second-order hyperbolic equation with anintegral overdetermination condition. To study the solvability of the inverse problem,we first reduce the considered problem to an auxiliary system with trivial data andprove its equivalence (in a certain sense) to the original problem. Then using the Banachfixed point principle, the existence and uniqueness of a solution to this system is shown.Further, on the basis of the equivalency of these problems the existence and uniquenesstheorem for the classical solution of the inverse coefficient problem is proved for thesmaller value of time.