On the nonlocal boundary value problem for the elliptic differential equations with integral type Samarskii-Ionkin conditions

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The present paper is devoted to the study of the abstract nonlocal boundary value problem with integral type Samarskii–Ionkin conditions for the differential equation of elliptic type \[\hspace{-6em}
-u''(t)+Au(t)=f(t)\quad (0\leq t\leq T),\quad u\left( 0\right)
=\varphi,\quad u'\left( 0\right) =u'\left( T\right)
+\int\limits_{0}^{T}\alpha \left( s\right) u(s)ds+\psi.\quad\] in an arbitrary Banach space \(E\) with the positive operator \(A\). The well-posedness of this problem in various Banach spaces is established. In applications, theorems on the well-posedness of several nonlocal boundary value problems for elliptic equations with integral type Samarskii–Ionkin conditions are proved.

作者简介

Allaberen Ashyralyev

Bahcesehir University; RUDN University; Institute of Mathematics and Mathematical Modeling

编辑信件的主要联系方式.
Email: allaberen.ashyralyev@eng.bau.edu.tr
Istanbul, Turkiye; Moscow, Russia; Almaty, Kazakhstan

Ayman Hamad

University of Benghazi

Email: ayman.hamad@uob.edu.ly
Elmarj, Libya

参考

  1. Дукенбаева А.А. Об одной обобщенной задаче типа Самарского-Ионкина для уравнения Пуассона в круге// Мат. ж.- 2018.-18, № 1.- C. 78-87.
  2. Ионкин Н.И. Решение одной краевой задачи теории теплопроводности с неклассическим краевым условием// Дифф. уравн.-1977.- 13, № 2. -C. 294-304.
  3. Ионкин Н.И. Об устойчивости одной задачи теории теплопроводности с неклассическим краевым условием// Дифф. уравн.-1979.- 15, № 7. -C. 1279-1283.
  4. Самарский А.А. О некоторых проблемах теории дифференциальных уравнений// Дифф. уравн.- 1980.-16, № 11.-C. 1925-1935.
  5. СОболевский П.Е. Разностные методы приближенного решения дифференциальных уравнений.- Воронеж: ВГУ, 1975.
  6. Ashyralyev A. On well-posedness of the nonlocal boundary value problems for elliptic equations// Numer. Funct. Anal. Optim. -2003.- 24, № 1-2.-C. 1-15.
  7. Ashyralyev A. A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space// J. Math. Anal. Appl. -2008.- 344, № 1.- C. 557-573.
  8. Ashyralyev A., Agirseven D., Agarwal R.P. Stability estimates for delay parabolic differential and difference equations// Appl. Comput. Math.- 2020.-19, № 2.- C. 175-204.
  9. Ashyralyev A., Hamad A. On the well-posedness of elliptic equations with nonlocal boundary conditions// TWMS J. Pure Appl. Math. - 2025.- 16, № 1.
  10. Ashyralyev A., Ozturk E. On a difference scheme of fourth order of accuracy for the Bitsadze-Samarskii type nonlocal boundary value problem// Math. Methods Appl. Sci. - 2013.- 36, № 8.-C. 936-955.
  11. Ashyralyev A., Sarsanbi A. Well-posedness of a parabolic equation with involution// Numer. Funct. Anal. Optim. -2017.- 38, № 10.-C. 1295-1305.
  12. Ashyralyev A., Sobolevskii P.E. New Difference Schemes for Partial Differential Equations.- Basel- Boston-Berlin : Birkhauser, 2004.
  13. Ashyralyev A., Tetikoglu F. FDM for elliptic equations with Bitsadze-Samarskii-Dirichlet conditions// Abst. Appl. Anal. -2012.- 2012.- 454831.
  14. Ashyralyev A., Tetikoglu F. A note on Bitsadze-Samarskii type nonlocal boundary value problems: wellposedness// Numer. Funct. Anal. Optim.- 2013.-34, № 9.- C. 939-975.
  15. Ashyralyyev C. Numerical solution to Bitsadze-Samarskii type elliptic overdetermined multipoint NBVP// Bound. Value Probl.- 2017.- 2017.-74.
  16. Ashyralyyev C. Stability estimates for solution of Neumann-type overdetermined elliptic problem// Numer. Funct. Anal. Optim. -2017.- 38, № 10.- C. 1226-1243.
  17. Ashyralyyev C., Akkan Y. Numerical solution to inverse elliptic problem with neumann type overdetermination and mixed boundary conditions// Electron. J. Differ. Equ. -2015.- 2015.- 188.
  18. Avalishvili G., Avalishvili M. Nonclassical problem with integral boundary conditions for elliptic system// Complex Var. Elliptic Equ. -2018.- 63, № 6.-C. 836-853.
  19. Ciupaila R., Sapagovas M., Stikoniene˙ O.ˇ Numerical solution of nonlinear elliptic equation with nonlocal condition// Nonlinear Anal. Model. Control-2013.-18, № 4.- C. 412-426.
  20. Gasimova Kh.A. On the Dirichlet problem for a class of non-uniformly elliptic equations with measure data// Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci.- 2023.-43, № 4.- C. 72-84.
  21. Il’in V.A., Kritskov L.V. Properties of spectral expansions corresponding to non-self-adjoint differential operators// J. Math. Sci. (N.Y) -2003.- 116, № 5.- C. 3489-3550.
  22. Kadirkulov B.J., Kirane M. On solvability of aboundary value problem for the Poisson equation with a nonlocal boundary operator// Acta Math. Sci. -2016.- 35.- C. 970-980.
  23. Karachik V.V., Turmetov B. Kh. On solvability of some nonlocal boundary value problems for biharmonic equation// Math. Slovaca-2020.-70, № 2. -C. 329-342.
  24. Kirane M., Torebek B.T. On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions// Math. Methods Appl. Sci. - 2016.- 39.- C. 1121-1128.
  25. Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems.- Basel-Boston-Berlin: Birkhauser, 1995.
  26. Pulkina L.S. Nonlocal problems for hyperbolic equations with degenerate integral conditions// Electron. J. Differ. Equ. -2016.-2016.-193.
  27. Sadybekov M.A., Dukenbayeva A.A. On boundary value problem of the Samarskii-Ionkin type for the Laplace operator in a ball// Kazakh Math. J. -2020.-20, № 1. -C. 84-94.
  28. Sadybekov M.A., Dukenbayeva A.A. On boundary value problems of the Samarskii-Ionkin type for the Laplace operator in a ball// Int. J. Complex Var. Elliptic Equ. -2022.-67, № 2. -C. 369-383.
  29. Sadybekov M.A., Dukenbayeva A.A., Yessirkegenov N.A., “On a generalised Samarskii-Ionkin typeproblem for the Poisson equation,” In: Algebra, Complex Analysis, and Pluripotential Theory, Springer, Cham, pp. 207-216.
  30. Sadybekov M.A., Turmetov B.Kh., Torebek B.T. Solvability of nonlocal boundary-value problems for the Laplace equation in the ball// Electron. J. Differ. Equ. -2014.- 2014.-157.
  31. Sapagovas M., Griskoniene V., Stikoniene˙ O.ˇ Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition// Nonlinear Anal. Model. Control-2017.- 22, № 4. -C. 489-504.
  32. Sapagovas M., Stikoniene O., Ciupaila R., Joksiene Z. Convergence of iterative methods for elliptic equations with integral boundary conditions// Electron. J. Differ. Equ. -2016.-2016.-118.
  33. Shakhmurov V., Musaev H. Nonlocal separable elliptic equations and applications// TWMS J. Pure Appl. Math. -2024.-15, № 2.- C. 257-268.
  34. Skubachevskii A.L. Elliptic Functional Differential Equations and Applications.- Basel-Boston-Berlin: Birkhauser, 1997.
  35. Stikoniene O., Sapagovas M., Ciupaila R. On iterative methods for some elliptic equations with nonlocal conditions// Nonlinear Anal. Model. Control- 2014.- 19, № 3.-C. 517-535.
  36. Triebel H. Interpolation Theory, Function Spaces, Differential Operators.-Amsterdam-New York: NorthHolland, 1978.
  37. Turmetov B.Kh., Karachik V.V. On solvability of some boundary value problems for a biharmonic equation with periodic conditions// Filomat-2018.-32, № 3.-C. 947-953.
  38. Turmetov B.Kh. Generalization of the Robin problem for the Laplace equation// Differ. Equ. - 2019.- 55, № 9.- C. 1134-1142.

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