RIQUET PROBLEM FOR ONE MODEL EQUATION OF THE 4TH ORDER HYPERBOLIC TYPE

  • I. M. Aleksandrovych Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • S. I. Lyashko Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • V. I. Lyashko National University «Kyiv-Mohyla Academy»
  • N. I. Lyashko V. M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv, Ukraine
  • M. V.–S. Sidorov Faculty of Sociology, Taras Shevchenko National University of Kyiv
Keywords: integral operators, regular solutions, equations of higher orders, boundary value problem

Abstract

Integral operators that transform arbitrary functions into regular solutions of hyperbolic equations of the second and higher orders are applied to solving boundary value problems. In particular, the Riquet problem for the Euler–Poisson–Darboux equation of the 4th order is posed and solved.

References

Aleksandrovich I. N., Zrazhevskaya V. F. The Cauchy problem and characteristic problem for one class of linear high-order hyperbolical equations. Doklady Acad. Nauk Ukr. 1991. No 4. P. 18–22.

Aleksandrovich I. M., Sydorov M. V.-S. Iterative equation of Euler–Poisson–Darboux type. Visnyk Kyiv. Univer., Fiz-Mat Seriya, 1999, No. 4, P. 75–81.

Aleksandrovich I. M., Sydorov M. V.-S. The Cauchy problem for a high-order telegraph equation. Journal of Numerical and Applied Mathematics, 1999, No. 1 (84), 16–24.

Aleksandrovich I. M., Bondar O. S., Lyashko S. I., Lyashko N. I., Sydorov M. V.-S. Integral Operators that Determine the Solution of an Iterated Hyperbolic-Type Equation. Cybernetics and Systems Analysis. 2020. No. 56. P. 401–409. https://doi.org/10.1007/s10559-020-00256-3

Sandrakov G. V., Lyashko S. I., Bondar E. S., Lyashko N. I. Modeling and optimization of microneedle systems. Journal of Automation and Information Sciences. 2019. Volume 51. Issue 6. P. 1–11. https://doi.org/10.1615/JAutomatInfScien.v51.i6.10

Aleksandrovich I. M., Molodtsov O. I. Differential mapping of hyperbolic equations. Visnyk Kyiv. Univer., Fiz-Mat Series, 2016. No 2. P. 98–104.

Lyashko I. I., Sydorov M. V.-S., Alexandrovich I. M. Inversion of some integral equations. Journal on Numerical and Applied Mathematics, 2004, No. 2, 25–30.

Published
2023-02-02
How to Cite
Aleksandrovych, I., Lyashko, S., Lyashko, V., Lyashko, N., & Sidorov, M. (2023). RIQUET PROBLEM FOR ONE MODEL EQUATION OF THE 4TH ORDER HYPERBOLIC TYPE. Journal of Numerical and Applied Mathematics, 1(2), 8-12. https://doi.org/10.17721/2706-9699.2022.2.01