Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

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dc.authorid0000-0001-6725-5663en_US
dc.contributor.authorZhuo, L.
dc.contributor.authorLesnic, D.
dc.contributor.authorIsmailov, M. I.
dc.contributor.authorTekin, İbrahim
dc.contributor.authorMeng, S.
dc.date.accessioned2021-03-20T20:12:27Z
dc.date.available2021-03-20T20:12:27Z
dc.date.issued2019
dc.departmentBTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractDiffusion processes with reaction generated by a nonlinear source are commonly encountered in practical applications related to ignition, pyrolysis and polymerization. In such processes, determining the intensity of reaction in time is of crucial importance for control and monitoring purposes. Therefore, this paper is devoted to such an identification problem of determining the time-dependent coefficient of a nonlinear heat source together with the unknown heat flux at an inaccessible boundary of a one-dimensional slab from temperature measurements at two sensor locations in the context of nonlinear transient heat conduction. Local existence and uniqueness results for the inverse coefficient problem are proved when the first three derivatives of the nonlinear source term are Lipschitz continuous functions. Furthermore, the conjugate gradient method (CGM) for separately reconstructing the reaction coefficient and the heat flux is developed. The ill-posedness is overcome by using the discrepancy principle to stop the iteration procedure of CGM when the input data is contaminated with noise. Numerical results show that the inverse solutions are accurate and stable.en_US
dc.description.sponsorshipChina Scholarship Council (CSC)China Scholarship Council; Major State Basic Research Development Program of China (973 Program)National Basic Research Program of China [2015CB655200]en_US
dc.description.sponsorshipL. Zhuo would like to acknowledge the China Scholarship Council (CSC) for supporting his visiting to the University of Leeds. S. Meng would like to acknowledge the support from the Major State Basic Research Development Program of China (973 Program) (Grant No. 2015CB655200).en_US
dc.identifier.doi10.1080/00207160.2018.1556790en_US
dc.identifier.endpage2099en_US
dc.identifier.issn0020-7160
dc.identifier.issn1029-0265
dc.identifier.issue10en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage2079en_US
dc.identifier.urihttp://doi.org/10.1080/00207160.2018.1556790
dc.identifier.urihttps://hdl.handle.net/20.500.12885/568
dc.identifier.volume96en_US
dc.identifier.wosWOS:000475440700011en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorTekin, İbrahim
dc.language.isoenen_US
dc.publisherTaylor & Francis Ltden_US
dc.relation.ispartofInternational Journal Of Computer Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectInverse heat source problemen_US
dc.subjectinverse heat conduction problemen_US
dc.subjectnonlinear sourceen_US
dc.subjectconjugate gradient methoden_US
dc.subjecteigenfunction series expansionen_US
dc.titleDetermination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problemen_US
dc.typeArticleen_US

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