An inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation

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dc.authorid0000-0001-5247-2913
dc.authorid0000-0001-6725-5663
dc.contributor.authorHuntul, Mousa J.
dc.contributor.authorTekin, Ibrahim
dc.date.accessioned2026-01-24T12:29:15Z
dc.date.available2026-01-24T12:29:15Z
dc.date.issued2023
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this article, simultaneous identification of the time-dependent lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge of additional measurements is studied. Existence and uniqueness of the solution is proved by means of the contraction mapping on a small time interval. Since the governing equation is yet ill-posed (very slight errors in the time-average temperature input may cause relatively significant errors in the output potential and source terms), we need to regularize the solution. Therefore, regularization is needed for the retrieval of unknown terms. The 2D problem is discretized using the alternating direction explicit (ADE) method and reshaped as non-linear least squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Finally, we present a numerical example to demonstrate the accuracy and efficiency of the proposed method. Our numerical results show that the ADE is an efficient and unconditionally stable scheme for reconstructing the potential and source coefficients from minimal data which makes the solution of the inverse problem (IP) unique.
dc.identifier.doi10.15672/hujms.1118138
dc.identifier.endpage1599
dc.identifier.issn2651-477X
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85176603445
dc.identifier.scopusqualityQ2
dc.identifier.startpage1578
dc.identifier.urihttps://doi.org/10.15672/hujms.1118138
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5232
dc.identifier.volume52
dc.identifier.wosWOS:001099204100001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherHacettepe Univ, Fac Sci
dc.relation.ispartofHacettepe Journal of Mathematics and Statistics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260121
dc.subject. existence and uniqueness
dc.subjectcontraction mapping
dc.subject2D parabolic equation
dc.subjectinverse identification problem
dc.subjectnonlinear optimization
dc.subjectTikhonov regularization
dc.titleAn inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation
dc.typeArticle

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