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Optimal control of a class of third-grade-Voigt equations

2025-11Artigo científico Acesso aberto
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dc.contributor.authorKinra, Kush
dc.contributor.authorCipriano, Fernanda
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblSpringer International Publishing
dc.date.accessioned2025-10-30T21:49:50Z
dc.date.available2025-10-30T21:49:50Z
dc.date.issued2025-11
dc.descriptionFunding Information: Open access funding provided by FCT|FCCN (b-on). This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications). Publisher Copyright: © The Author(s) 2025.
dc.description.abstractThis work aims to understand the velocity tracking control problem for a class of non-Newtonian fluids. We introduce the third-grade-Voigt equations in the two-dimensional torus T2 and prove the existence and uniqueness of the solution. Then, we show the existence and uniqueness of solution to the corresponding linearized state equation and adjoint equation. Additionally, we provide a suitable stability result for the state equation and demonstrate that the Gateaux derivative of the control-to-state mapping agrees with the solution of the linearized state equation. Next, we establish the first order optimality conditions and show the existence of an optimal solution. Ultimately, we are able to provide a uniqueness result for the coupled system consisting of the adjoint equation, the state equation, and the first order optimality condition. Therefore, under appropriate conditions on the data, the uniqueness of the optimal solution holds.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent53
dc.format.extent848475
dc.identifier.doi10.1007/s00030-025-01129-4
dc.identifier.issn1021-9722
dc.identifier.otherPURE: 133977394
dc.identifier.otherPURE UUID: f4b02dc9-9d8b-467b-8b27-0b0518441560
dc.identifier.otherScopus: 105015195009
dc.identifier.otherWOS: 001564684400001
dc.identifier.otherORCID: /0000-0001-6385-8846/work/195655279
dc.identifier.urihttp://hdl.handle.net/10362/189907
dc.identifier.urlhttps://www.scopus.com/pages/publications/105015195009
dc.identifier.urlhttps://www.webofscience.com/wos/woscc/full-record/WOS:001564684400001
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
dc.relationCenter for Mathematics and Applications
dc.subjectOptimal control
dc.subjectPDEs
dc.subjectThird-grade-Voigt equations
dc.subjectAnalysis
dc.subjectApplied Mathematics
dc.titleOptimal control of a class of third-grade-Voigt equationsen
dc.typejournal article
degois.publication.firstPage1
degois.publication.lastPage53
degois.publication.titleNonlinear Differential Equations and Applications
degois.publication.volume32
dspace.entity.typePublication
oaire.awardNumberUIDB/00297/2020
oaire.awardNumberUIDP/00297/2020
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
oaire.fundingStreamConcurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublication6d719021-6aee-40c1-a930-d811c01c997d
relation.isProjectOfPublication65d392f7-8781-4d70-b9f3-069b07d4a311
relation.isProjectOfPublication.latestForDiscovery6d719021-6aee-40c1-a930-d811c01c997d

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