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


Imanbetova A. Sarsenbi A. Seilbekov B.
August 2023Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2023#11Issue 15

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.

eigenfunction , fourth-order hyperbolic equations , inverse problem , the Fourier method , the Riesz basis

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Department of Mathematics, South Kazakhstan University of the Name of M. Auezov, Shymkent, 160000, Kazakhstan
Scientific Institute “Theoretical and Applied Mathematics”, South Kazakhstan University of the Name of M. Auezov, Shymkent, 160000, Kazakhstan
Department of Mathematics, South Kazakhstan State Pedagogical University, Shymkent, 160000, Kazakhstan

Department of Mathematics
Scientific Institute “Theoretical and Applied Mathematics”
Department of Mathematics

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