Abstract

In this paper, the well-posedness theorem on the parabolic differential equation with involution and nonlocal conditions is considered. The stable difference scheme for the approximate solution of this problem is presented. Numerical results are given.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 2
Year: 2021

DOI: 10.12732/ijam.v34i2.15

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

1. [1] M. Sapagovas and K. Akubeliene, Alternating direction method for twodimensional parabolic equation with nonlocal integral condition, Nonlinear Anal.Model., 17, No 1 (2012), 91-98.
2. [2] N. Gordeziani, P. Natani and P.E. Ricci, Finite-difference methods for solution of nonlocal boundary value problems, Comput. Math. with Appl., 50 (2005), 13331344.
3. [3] M. Dehghan, On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation, Numer. Methods Partial Differ. Equ., 21, No 1 (2005), 24-40.
4. [4] M. Dehghan, A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications, Numer. Methods Partial Differ. Equ., 22, No 1 (2006), 220-257.
5. [5] F.F. Ivanauskas, Yu.A. Novitski andM.P. Sapagovas, On the stability of an explicit difference scheme for hyperbolic equations with nonlocal boundary conditions, Differ. Equ., 49, No 7 (2013), 849-856.
6. [6] F. Zouyed, F. Rebbani and N. Boussetila, On a class of multitime evolution equations with nonlocal initial conditions, Abstr. Appl. Anal., 2007 (2007), Art. ID 16938, 26 pages.
7. [7] A. Boucherif and R. Precup, Semilinear evolution equations with nonlocal initial conditions, Dyn. Syst. Appl., 16, No 3 (2007), 507-516.
8. [8] J. Jachimaviciene, M. Sapagovas, A. Stikonas and O. Stikoniene, On the stability of explicit finite difference schemes for a pseudoparabolic equation with nonlocal conditions, Nonlinear Anal.-Model., 19, No 2 (2014), 225-240.
9. [9] A. Ashyralyev, Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces, J. Evol. Equ., 6, No 1 (2006), 1-28.
10. [10] A. Ashyralyev, A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space, J. Math. Anal. Appl., 344, No 1 (2008), 557-573.
11. [11] P.E. Sobolevskii, Coerciveness inequalities for abstract parabolic equations, Dokl. Akad. Nauk SSSR, 197, No 1 (1964), 52-55 (in Russian).
12. [12] V.P. Anosov and P.E. Sobolevskii, The coercive solvability of parabolic equations, Mat. Zametki, 11, No 2 (1972), 409-419 (in Russian).
13. [13] A. Ashyralyev and A.M. Sarsenbi, Well-posedness of an elliptic equation with involution, Electron. J. Differ. Equ., 284 (2015), 1-8.
14. [14] A. Ashyralyev and A. Sarsenbi, Well-posedness of a parabolic equation with involution, Numer. Funct. Anal. Optim., 38, No 10 (2017), 1295-1304.
15. [15] A. Ashyralyev, B. Karabaeva and A.M. Sarsenbi, Stable difference scheme for the solution of an elliptic equation with involution, In: AIP Conf. Proc., 1759 (3rd Int. Conf. on Analysis and Applied Mathematics (ICAAM2016), Almaty, Kazakhstan, Sep. 7-10, 2016) (Ed. by: A. Ashyralyev and A. Lukashov), Amer. Inst. Phys. (2016), Art. 020111.
16. [16] A. Cabada and F. Tojo, Differential Equations with Involutions, Atlantis Press (2015).