Identification of boundary conditions of a differential operator

  • B. E. Kanguzhin al-Farabi Kazakh National University
  • G. Dairbayeva al-Farabi Kazakh National University
  • Zh. Madibaiuly Institute of Mechanics and Mechanical Engineering named after Academician U.A. Zholdasbekov

Abstract

This pap er consists of three parts. To achieve uniqueness of the solution of the B max u = hindicated inhomogeneous equation, it is necessary to narrow the domain of definition of themaximum op erator. The narrowing usually o ccurs due to b oundary conditions. Thus, a class ofcorrect restrictions of the maximum op erator arises. In the second part of the article, we givethe pro of of Theorem 1 and the justification of the pro cedure for recovering b oundary functions{ σ 2 ( t ) , . . . , σ n ( t ) } . In the third part of the article, we separately consider the case of reconstructingtwo-point boundary value problems from a finite set of eigenvalues and give illustrative numericalexamples of approximate calculations of the coefficients of the boundary conditions. Note that theproblem of recovering boundary functions { σ 2 ( t ) , . . . , σ n ( t ) } from the procedure we have proposed,the linear problem. This fact is not obvious if the initial set of boundary functions is restored { σ j k } .

References

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Published
2019-10-28
How to Cite
KANGUZHIN, B. E.; DAIRBAYEVA, G.; MADIBAIULY, Zh.. Identification of boundary conditions of a differential operator. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 103, n. 3, p. 13-18, oct. 2019. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/658>. Date accessed: 22 oct. 2020. doi: https://doi.org/10.26577/JMMCS-2019-3-22.
Keywords boundary conditions, correct narrowing