Stabilization of higher order Schrödinger equations on a finite interval: Part I

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buir.contributor.authorÖzsarı, Türker
buir.contributor.orcidÖzsarı, Türker|0000-0003-4240-5252
dc.citation.epage919en_US
dc.citation.issueNumber4en_US
dc.citation.spage861en_US
dc.citation.volumeNumber10en_US
dc.contributor.authorBatal, Ahmet
dc.contributor.authorÖzsarı, Türker
dc.contributor.authorYılmaz, K.C.
dc.coverage.spatialUnited Statesen_US
dc.date.accessioned2022-02-09T11:12:41Z
dc.date.available2022-02-09T11:12:41Z
dc.date.issued2021-12
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe study the backstepping stabilization of higher order linear and nonlinear Schrödinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a prescribed rate of decay. The construction of the backstepping kernel is based on a challenging successive approximation analysis. This contrasts with the case of second order pdes. Second, we consider the case where the full state of the system cannot be measured at all times but some partial information such as measurements of a boundary trace are available. For this problem, we simultaneously construct an observer and the associated backstepping controller which is capable of stabilizing the original plant. Wellposedness and regularity results are provided for all pde models. Although the linear part of the model is similar to the KdV equation, the power type nonlinearity brings additional difficulties. We give two examples of boundary conditions and partial measurements. We also present numerical algorithms and simulations verifying our theoretical results to the fullest extent. Our numerical approach is novel in the sense that we solve the target systems first and obtain the solution to the feedback system by using the bounded invertibility of the backstepping transformation.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2022-02-09T11:12:41Z No. of bitstreams: 1 Stabilization_of_higher_order_Schrödinger_equations_on_a_finite_interval_Part_I.pdf: 2707530 bytes, checksum: b0f036d5b2667f281e0e50e203be6d8d (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-09T11:12:41Z (GMT). No. of bitstreams: 1 Stabilization_of_higher_order_Schrödinger_equations_on_a_finite_interval_Part_I.pdf: 2707530 bytes, checksum: b0f036d5b2667f281e0e50e203be6d8d (MD5) Previous issue date: 2021-12en
dc.identifier.doi10.3934/EECT.2020095en_US
dc.identifier.issn2163-2472
dc.identifier.urihttp://hdl.handle.net/11693/77168
dc.language.isoEnglishen_US
dc.publisherAIMS Pressen_US
dc.relation.isversionofhttps://dx.doi.org/10.3934/EECT.2020095en_US
dc.source.titleEvolution Equations & Control Theoryen_US
dc.subjectHigher order Schrödinger equationen_US
dc.subjectBacksteppingen_US
dc.subjectStabilizationen_US
dc.subjectObserveren_US
dc.subjectBoundary controlleren_US
dc.subjectExponential stabilityen_US
dc.titleStabilization of higher order Schrödinger equations on a finite interval: Part Ien_US
dc.typeArticleen_US

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