Regularization of a Multidimensional Inverse Problem With the D’alembert Operator, Degenerating Into a Systemof Volterra Equations

In the field of wave theory, in problems of hereditary environment, etc., various classes of inverse problems are encountered, and in the study the most important role is played by the questions of uniqueness of the solution and regularizability of the original problems in certain spaces. In this regard, we study a multidimensional inverse problem with the D’Alembert operator in an unbounded domain where the system of Volterra integral equations of the first and third kind degenerates. Further, in order to prove the regularizability of the original problem in the Banach vector space, we apply a variant of the system regularization method.