REGULARIZATION OF THE INVERSE PROBLEM WITH THE D’ALEMBERT OPERATOR IN AN UNBOUNDED DOMAIN DEGENERATING INTO A SYSTEM OF INTEGRAL EQUATIONS OF VOLTERRA TYPE
Abstract
In this paper, we study the inverse problem for the wave equation with the second-order d’Alembert operator in an unbounded domain in a space with a non-uniform metric. For physical applications, inverse problems for second-order partial differential equations are of particular interest. Such inverse problems are encountered in the study of wave processes, processes of electromagnetic interactions, as well as in various reduction processes. Moreover, if there are external acting forces with respect to the indicated equations that allow additional information about the solution of the original equations, then we obtain classes of inverse problems of a coefficient nature with the d’Alembert operator, which are of particular interest to scientists in this field, in which the results of this article are relevant. Also, the relevance of the problem under study is due to the fact that it is an inverse problem, where the sought quantities are the causes of some known consequences of a particular process. Whereas for direct problems, the methods for solving are well known. Thus, this paper provides a solution to the inverse problem of mathematical physics with a hyperbolic operator and generalizes existing results.
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