APPROXIMATION OF AN OPTIMAL BV-CONTROL PROBLEM IN THE COEFFICIENT FOR THE p(x)-LAPLACE EQUATION

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dc.contributor.authorAydin, Ismail
dc.contributor.authorKogut, Peter
dc.date.accessioned2025-03-23T19:16:54Z
dc.date.available2025-03-23T19:16:54Z
dc.date.issued2024
dc.departmentSinop Üniversitesi
dc.description.abstractWe study a Dirichlet optimal control problem for a quasilinear monotone elliptic equation with the so-called weighted p(x)-Laplace operator. The coefficient of the p(x)-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the admissible controls. In order to handle the inherent degeneracy of the p(x)-Laplacian, we use a special two-parametric regularization scheme. We derive existence and uniqueness of variational V -solutions to the underlying boundary value problem and the corresponding optimal control problem. Further we discuss the asymptotic behaviour of the solutions to regularized problems on each (ε, k)-level as the parameters tend to zero and infinity, respectively. The characteristic feature of the considered OCP is the fact that the exponent p(x) is assumed to be Lebesgue-measurable, and we do not impose any additional assumptions on p(x) like to be a Lipschitz function or satisfy the so-called log-Hölder continuity condition. © I. Aydin, P. Kogut, 2024.
dc.identifier.doi10.15421/142414
dc.identifier.endpage204
dc.identifier.issn2617-0108
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85211610516
dc.identifier.scopusqualityQ3
dc.identifier.startpage175
dc.identifier.urihttps://doi.org/10.15421/142414
dc.identifier.urihttps://hdl.handle.net/11486/4210
dc.identifier.volume32
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherOles Honchar Dnipro National University
dc.relation.ispartofJournal of Optimization, Differential Equations and their Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_Scopus_20250323
dc.subjectcontrol in coefficients
dc.subjectNonlinear Dirichlet problem
dc.subjectoptimal control
dc.subjectp(x)-Laplace operator
dc.subjectvariable exponent
dc.titleAPPROXIMATION OF AN OPTIMAL BV-CONTROL PROBLEM IN THE COEFFICIENT FOR THE p(x)-LAPLACE EQUATION
dc.typeArticle

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