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On Solvability of Some Boundary Value Problems with Involution for the Biharmonic Equation

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Functional Analysis in Interdisciplinary Applications—II (ICAAM 2018)

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Abstract

In this paper we study new classes of well-posed boundary-value problems for the biharmonic equation. The considered problems are Bitsadze–Samarskii type nonlocal boundary value problems. The investigated problems are solved by reducing them to the Neumann and Dirichlet type problems. In this paper, theorems on existence and uniqueness of the solution are proved, and exact conditions for solvability of the problems are found. In addition, integral representations of the solution are obtained.

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Acknowledgements

The work was supported by Act 211 of the Government of the Russian Federation, contract no.02.A03.21.0011, and by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (grant no. AP05131268).

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Authors and Affiliations

  1. South Ural State University, Prosp. Lenina 76, Chelyabinsk, 454080, Russian Federation

    Valery V. Karachik

  2. Akhmet Yassawi University, 29 B.Sattarkhanov avenue, Turkistan, 161200, Kazakhstan

    Batirkhan Kh. Turmetov

Authors
  1. Valery V. Karachik
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  2. Batirkhan Kh. Turmetov
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Correspondence to Batirkhan Kh. Turmetov .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Near East University, Mersin, Turkey

    Allaberen Ashyralyev

  2. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  3. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

  5. Department of Mathematics, Nazarbayev University, Astana, Kazakhstan

    Durvudkhan Suragan

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Karachik, V.V., Turmetov, B.K. (2021). On Solvability of Some Boundary Value Problems with Involution for the Biharmonic Equation. In: Ashyralyev, A., Kalmenov, T.S., Ruzhansky, M.V., Sadybekov, M.A., Suragan, D. (eds) Functional Analysis in Interdisciplinary Applications—II. ICAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 351. Springer, Cham. https://doi.org/10.1007/978-3-030-69292-6_5

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