Inverse Problem for a Fourth-Order Hyperbolic Equation with a Complex-Valued Coefficient

Asselkhan Imanbetova, Abdissalam Sarsenbi and Bolat Seilbekov ()
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Asselkhan Imanbetova: Department of Mathematics, South Kazakhstan University of the Name of M. Auezov, Shymkent 160000, Kazakhstan
Abdissalam Sarsenbi: Scientific Institute “Theoretical and Applied Mathematics”, South Kazakhstan University of the Name of M. Auezov, Shymkent 160000, Kazakhstan
Bolat Seilbekov: Scientific Institute “Theoretical and Applied Mathematics”, South Kazakhstan University of the Name of M. Auezov, Shymkent 160000, Kazakhstan

Mathematics, 2023, vol. 11, issue 15, 1-14

Abstract: This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form of a Fourier series in terms of the eigenfunctions of a non-self-adjoint fourth-order ordinary differential operator. The proofs of the uniform convergence of the Fourier series are based on estimates of the norms of the derivatives of the eigenfunctions of a fourth-order ordinary differential operator and the uniform boundedness of the Riesz bases of the eigenfunctions.

Keywords: fourth-order hyperbolic equations; inverse problem; eigenfunction; the Riesz basis; the Fourier method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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