INVERSE PROBLEM OF DETERMINING THE SOURCE IN ONE HYPERBOLIC EQUATION THIRD ORDER

Abstract

In this paper, we study the time-dependent inverse problem of determining a solution and an unknown source for a third-order linear hyperbolic equation. In inverse problems, along with the initial data (in our case), additional information is given. As additional information for solving the inverse problem, the values of the solution of the problem at the interior point are given. Inverse problems of determining the right side of a differential equation arise in the mathematical modeling of some physical processes, in the case when it is required to restore the action of external sources. An existence and uniqueness theorem for the solution of the inverse problem is proved. The proof is based on the derivation of a linear system of integral equations of the Volterra type of the second kind and the proof of its solvability.