Inverse problem for time dependent coefficients in the higher order pseudo-parabolic equation

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dc.contributor.authorHuntul, M. J.
dc.contributor.authorTekin, I.
dc.date.accessioned2026-01-24T12:26:38Z
dc.date.available2026-01-24T12:26:38Z
dc.date.issued2025
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this paper, we considered an inverse problem of recovering the time dependent potential and force coefficients in the third order pseudoparabolic equation from nonlocal integral observations. Existence and uniqueness of the solution are proved by means of the contraction principle on a small time interval. The stability results for the inverse problem is presented. The unique solvability theorem for this inverse problem is proved. However, since the governing equation is yet ill-posed (very slight errors in the integral input may cause relatively significant errors in the output potential and heat source terms), we need to regularize the solution. Therefore, to get a stable solution, a regularized cost function is to be minimized for retrieval of the unknown terms. The third order pseudoparabolic problem is discretized using the cubic B-spline (CB-spline) collocation technique and reshaped as nonlinear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Both analytical and perturbed data are inverted. Numerical outcomes for two benchmark test examples are reported and discussed. In addition, the von Neumann stability analysis for the proposed numerical approach has also been discussed.
dc.identifier.doi10.3934/mmc.2025017
dc.identifier.endpage257
dc.identifier.issn2767-8946
dc.identifier.issue3
dc.identifier.scopus2-s2.0-105012255795
dc.identifier.scopusqualityQ2
dc.identifier.startpage236
dc.identifier.urihttps://doi.org/10.3934/mmc.2025017
dc.identifier.urihttps://hdl.handle.net/20.500.12868/4826
dc.identifier.volume5
dc.identifier.wosWOS:001538104400001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofMathematical Modelling and Control
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260121
dc.subjectthird-order pseudo-parabolic equation
dc.subjectinverse problem
dc.subjectstability analysis
dc.subjectTikhonov regularization
dc.subjectnonlinear optimization
dc.titleInverse problem for time dependent coefficients in the higher order pseudo-parabolic equation
dc.typeArticle

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