Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations

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dc.authoridAshyralyev, Allaberen/0000-0002-4153-6624
dc.contributor.authorAshyralyev, Allaberen
dc.contributor.authorAgirseven, Deniz
dc.date.accessioned2024-06-12T11:14:02Z
dc.date.available2024-06-12T11:14:02Z
dc.date.issued2019
dc.departmentTrakya Üniversitesien_US
dc.description.abstractIn this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential problem for a semilinear hyperbolic equation with unbounded time delay term is established. In applications, the existence and uniqueness of bounded solutions of four problems for semilinear hyperbolic equations with time delay in unbounded term are obtained. For the approximate solution of this abstract differential problem, the two-step difference scheme of a first order of accuracy is presented. The mean theorem on the existence and uniqueness of a uniformly bounded solution of this difference scheme with respect to time stepsize is established. In applications, the existence and uniqueness of a uniformly bounded solutions with respect to time and space stepsizes of difference schemes for four semilinear partial differential equations with time delay in unbounded term are obtained. In general, it is not possible to get the exact solution of semilinear hyperbolic equations with unbounded time delay term. Therefore, numerical results for the solution of difference schemes for one and two dimensional semilinear hyperbolic equation with time delay are presented. Finally, some numerical examples are given to confirm the theoretical analysis.en_US
dc.description.sponsorshipRussian Foundation for Basic Research (RFBR) [16-01-00450]en_US
dc.description.sponsorshipThis research was funded by Russian Foundation for Basic Research (RFBR) grant number 16-01-00450.en_US
dc.identifier.doi10.3390/math7121163
dc.identifier.issn2227-7390
dc.identifier.issue12en_US
dc.identifier.scopus2-s2.0-85079612836en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.3390/math7121163
dc.identifier.urihttps://hdl.handle.net/20.500.14551/23781
dc.identifier.volume7en_US
dc.identifier.wosWOS:000506643400030en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMdpien_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSemilinear Problems With Delayen_US
dc.subjectHyperbolic Equationsen_US
dc.subjectDifference Schemeen_US
dc.subjectStabilityen_US
dc.subjectHilbert Spaceen_US
dc.subjectSchemesen_US
dc.subjectStabilityen_US
dc.subject1st-Orderen_US
dc.titleBounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equationsen_US
dc.typeArticleen_US

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