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Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms

Author

Listed:
  • Allaberen Ashyralyev

    (Department of Mathematics, Bahcesehir University, Istanbul 34353, Turkey
    Department of Mathematics, Peoples’ Friendship University of Russia, 117198 Moscow, Russia
    Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan)

  • Sa’adu Bello Mu’azu

    (Department of Mathematics, Faculty of Arts and Sciences, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey
    Department of Mathematics, Faculty of Physical Sciences, Kebbi State University of Science and Technology, Aliero P.O. Box 1144, Nigeria)

Abstract

In the present work, an initial boundary value problem (IBVP) for the semi-linear delay differential equation in a Banach space with unbounded positive operators is studied. The main theorem on the uniqueness and existence of a bounded solution (BS) of this problem is established. The application of the main theorem to four different semi-linear delay parabolic differential equations is presented. The first- and second-order accuracy difference schemes (FSADSs) for the solution of a one-dimensional semi-linear time-delay parabolic equation are considered. The new desired numerical results of this paper and their discussion are presented.

Suggested Citation

  • Allaberen Ashyralyev & Sa’adu Bello Mu’azu, 2023. "Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3470-:d:1214793
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    References listed on IDEAS

    as
    1. Deniz Agirseven, 2012. "Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-31, June.
    2. El-Sayed, A.M.A. & Gaafar, F.M., 2001. "Fractional-order differential equations with memory and fractional-order relaxation-oscillation model," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 12(3), pages 296-310.
    3. H. Chi & H. Poorkarimi & J. Wiener & S. M. Shah, 1989. "On the exponential growth of solutions to non-linear hyperbolic equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-7, January.
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