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Inverse Problem for the Sobolev Type Equation of Higher Order

Author

Listed:
  • Alyona Zamyshlyaeva

    (Department of Applied Mathematics and Programming, South Ural State University, 454080 Chelyabinsk, Russia)

  • Aleksandr Lut

    (Department of Applied Mathematics and Programming, South Ural State University, 454080 Chelyabinsk, Russia)

Abstract

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

Suggested Citation

  • Alyona Zamyshlyaeva & Aleksandr Lut, 2021. "Inverse Problem for the Sobolev Type Equation of Higher Order," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1647-:d:593404
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    References listed on IDEAS

    as
    1. Evgenii S. Baranovskii, 2020. "Strong Solutions of the Incompressible Navier–Stokes–Voigt Model," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
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    Cited by:

    1. Fasma Diele, 2022. "Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges," Mathematics, MDPI, vol. 10(2), pages 1-3, January.

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