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dc.contributor.authorErbay, Hüsnü Ata
dc.contributor.authorErkip, A.
dc.contributor.authorŞengül, Y.
dc.date.accessioned2020-11-03T08:23:15Z
dc.date.available2020-11-03T08:23:15Z
dc.date.issued2020-11-15
dc.identifier.issn0022-0396en_US
dc.identifier.urihttp://hdl.handle.net/10679/7056
dc.identifier.urihttps://www.sciencedirect.com/science/article/abs/pii/S0022039620303739
dc.description.abstractIn this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the sum of the strain and the strain rate. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.en_US
dc.description.sponsorshipTÜBİTAK
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relationinfo:turkey/grantAgreement/TUBITAK/116F093
dc.relation.ispartofJournal of Differential Equations
dc.rightsrestrictedAccess
dc.titleLocal existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticityen_US
dc.typeArticleen_US
dc.peerreviewedyesen_US
dc.publicationstatusPublisheden_US
dc.contributor.departmentÖzyeğin University
dc.contributor.authorID(ORCID 0000-0002-5167-609X & YÖK ID 119316) Erbay, Hüsnü Ata
dc.contributor.ozuauthorErbay, Hüsnü Ata
dc.identifier.volume269en_US
dc.identifier.issue11en_US
dc.identifier.startpage9720en_US
dc.identifier.endpage9739en_US
dc.identifier.wosWOS:000575391800023
dc.identifier.doi10.1016/j.jde.2020.06.052en_US
dc.subject.keywordsViscoelasticityen_US
dc.subject.keywordsStrain-limiting theoryen_US
dc.subject.keywordsInitial-value problemen_US
dc.subject.keywordsLocal existenceen_US
dc.identifier.scopusSCOPUS:2-s2.0-85087218740
dc.contributor.authorMale1
dc.relation.publicationcategoryArticle - International Refereed Journal - Institution Academic Staff


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