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

Allaberen Ashyralyev and Sa’adu Bello Mu’azu ()
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Allaberen Ashyralyev: Department of Mathematics, Bahcesehir University, Istanbul 34353, Turkey
Sa’adu Bello Mu’azu: Department of Mathematics, Faculty of Arts and Sciences, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey

Mathematics, 2023, vol. 11, issue 16, 1-14

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.

Keywords: bounded solution; delay parabolic equations; uniqueness and existence; unbounded delay term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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