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dc.contributor.authorBeyer, Horst Reinhard
dc.contributor.authorAksoylu, Burak
dc.contributor.authorÇeliker, Fatih
dc.date.accessioned2019-07-04T14:19:42Z
dc.date.available2019-07-04T14:19:42Z
dc.date.issued2016-06
dc.identifier.citationBeyer, H. R., Aksoylu, B., & Celiker, F. (2016). On a class of nonlocal wave equations from applications. Journal of Mathematical Physics, 57(6), 062902.en_US
dc.identifier.issn0022-2488
dc.identifier.otherArticle number 062902, number of pages 29
dc.identifier.urihttps://doi.org/10.1063/1.4953252
dc.identifier.urihttp://hdl.handle.net/20.500.11851/1685
dc.description.abstractWe study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain Rn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.en_US
dc.description.sponsorshipTUBITAK 2221 Fellowship for Visiting Scientist Programen_US
dc.language.isoengen_US
dc.publisherAmerican Institute of Physics Inc.en_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectFinite-Element-Methoden_US
dc.subject Long-Range Forcesen_US
dc.subject Peridynamic Theoryen_US
dc.subject Linear Elasticityen_US
dc.subject Global Existenceen_US
dc.subject Navier Equationen_US
dc.subject Blow-Upen_US
dc.subject Diffusionen_US
dc.subject Modelsen_US
dc.subject Approximationen_US
dc.titleOn a class of nonlocal wave equations from applicationsen_US
dc.typearticleen_US
dc.relation.journalJournal of Mathematical Physicsen_US
dc.contributor.departmentTOBB ETU, Faculty of Science and Literature, Department of Mathematicsen_US
dc.contributor.departmentTOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümütr_TR
dc.identifier.volume57
dc.identifier.issue6
dc.relation.tubitakinfo:eu-repo/grantAgreement/TÜBİTAK/TBAG/112T240en_US
dc.relation.tubitakinfo:eu-repo/grantAgreement/TÜBİTAK/MAG/112M891en_US
dc.relation.ecEuropean Commission Marie Curie Career Integration Grant [293978]en_US
dc.contributor.orcidhttps://orcid.org/0000-0002-7244-3340
dc.identifier.wosWOS:000379168200025
dc.identifier.scopus2-s2.0-84974803074
dc.contributor.tobbetuauthorAksoylu, Burak
dc.contributor.YOKid29230
dc.identifier.doi10.1063/1.4953252
dc.contributor.wosresearcherIDC-4948-2016
dc.contributor.ScopusAuthorID23979376500
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıtr_TR
dc.relation.internationalNational Science Foundation DMS [1016190]en_US
dc.relation.internationalNational Science Foundation DMS [1115280]en_US


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