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

Author

Listed:
  • Asselkhan Imanbetova

    (Department of Mathematics, South Kazakhstan University of the Name of M. Auezov, Shymkent 160000, Kazakhstan
    These authors contributed equally to this work.)

  • Abdissalam Sarsenbi

    (Scientific Institute “Theoretical and Applied Mathematics”, South Kazakhstan University of the Name of M. Auezov, Shymkent 160000, Kazakhstan
    These authors contributed equally to this work.)

  • Bolat Seilbekov

    (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)

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.

Suggested Citation

  • Asselkhan Imanbetova & Abdissalam Sarsenbi & Bolat Seilbekov, 2023. "Inverse Problem for a Fourth-Order Hyperbolic Equation with a Complex-Valued Coefficient," Mathematics, MDPI, vol. 11(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3432-:d:1212032
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