Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redefinition Conditions at the End of the Interval and Involution

In this paper, we consider an inhomogeneous hyperbolic type partial integrodifferential equation with degenerate kernel, two redefinition functions and involution.Intermediate data are used to find these redefinition functions. Dirichlet boundary conditions with respect to spatial variable are used. The Fourier method of separation ofvariables is applied. The countable system of functional-integral equations is obtained.Theorem on a unique solvability of countable system of functional-integral equations isproved. The method of successive approximations is used in combination with the methodof contraction mappings. The triple of solutions of the inverse problem is obtained inthe form of Fourier series. Absolute convergence of Fourier series is proved.

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