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Uniqueness Criterion for the Solution of Boundary-Value Problems for the Abstract Euler–Poisson–Darboux Equation on a Finite Interval

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Abstract

For the abstract Euler–Poisson–Darboux equation, boundary-value problems with Dirichlet and Neumann conditions are considered. The criterion for the uniqueness of the solution is established.

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References

  1. V. K. Ivanov, I. V. Mel’nikova, and A. I. Filinkov, Differential Operator Equations and Ill-Posed Problems (Nauka, Moscow, 1995) [in Russian].

    MATH  Google Scholar 

  2. S. I. Kabanikhin and O. I. Krivorot’ko, “A numerical method for solving the Dirichlet problem for the wave equation,” J. Appl. Industr. Math. 7 (2), 187–198 (2013).

    Article  MathSciNet  Google Scholar 

  3. V. I. Vasil’ev, A. M. Kardashevskii, and V. V. Popov, “Solution of the Dirichlet problem for the string oscillation equation by the conjugate gradient method,” Vestn. NEFU 12 (2), 43–50 (2015).

    Google Scholar 

  4. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].

    MATH  Google Scholar 

  5. A. V. Glushak, “Stabilization of the solution of the Dirichlet problem for an elliptic equation in a Banach space,” Differ. Equ. 33 (4), 513–517 (1997).

    MathSciNet  MATH  Google Scholar 

  6. A. V. Glushak, “On the solvability of boundary value problems for an abstract Bessel–Struve equation,” Differ. Equ. 55 (8), 1069–1076 (2019).

    Article  MathSciNet  Google Scholar 

  7. A. V. Glushak, V. I. Kononenko, and S. D. Shmulevich, “A singular abstract Cauchy problem,” Soviet Math. (Iz. VUZ) 30 (6), 78–81 (1986).

    MathSciNet  MATH  Google Scholar 

  8. A. V. Glushak, “O. A. Criterion for the solvability of the Cauchy problem for an abstract Euler–Poisson– Darboux equation,” Differ. Equ. 52 (1), 39–57 (2016).

    Article  MathSciNet  Google Scholar 

  9. G. Watson, A Treatise on the Theory of Bessel Functions (Cambridge Univ. Press, Cambridge, 1945).

    Google Scholar 

  10. A. N. Bogolyubov and V. V. Kravtsov, Problems in Mathematical Physics (Izd. Mosk. Univ., Moscow, 1998) [in Russian].

    Google Scholar 

  11. M. K. Kerimov, “Studies on the zeros of Bessel functions and methods for their computation,” Comput. Math. Math. Phys. 54 (9), 1337–1388 (2014).

    Article  MathSciNet  Google Scholar 

  12. K. B. Sabitov, “The Dirichlet problem for higher-order partial differential equations,” Math. Notes 97 (2), 255–267 (2015).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Belgorod National Research University, Belgorod, 308015, Russia

    A. V. Glushak

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  1. A. V. Glushak
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Correspondence to A. V. Glushak.

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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 821-831 https://doi.org/10.4213/mzm12790.

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Glushak, A.V. Uniqueness Criterion for the Solution of Boundary-Value Problems for the Abstract Euler–Poisson–Darboux Equation on a Finite Interval. Math Notes 109, 867–875 (2021). https://doi.org/10.1134/S0001434621050205

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  • DOI: https://doi.org/10.1134/S0001434621050205

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