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

Abstract

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 of variables is applied. The countable system of functional-integral equations is obtained. Theorem on a unique solvability of countable system of functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mappings. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Absolute convergence of Fourier series is proved.

Keywords

• inverse problem
• two redefinition functions
• final conditions at the endpoint of a segment
• intermediate data
• three parameters
• involution
• unique solvability

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