Existence of unattainable states for Schrödinger type flows on the half-line

buir.contributor.authorÖzsarı, Türker
buir.contributor.orcidÖzsarı, Türker|0000-0003-4240-5252
dc.citation.epage803en_US
dc.citation.issueNumber4
dc.citation.spage789
dc.citation.volumeNumber40
dc.contributor.authorÖzsarı, Türker
dc.contributor.authorKalimeris, Konstantinos
dc.date.accessioned2024-03-10T13:16:45Z
dc.date.available2024-03-10T13:16:45Z
dc.date.issued2023-12-01
dc.departmentDepartment of Mathematics
dc.description.abstractWe prove that the solutions of the Schrödinger and biharmonic Schrödinger equations do not have the exact boundary controllability property on the half-line by showing that the associated adjoint models lack observability. We consider the framework of L2 boundary controls with data spaces H−1(R+) and H−2(R+) for the classical and biharmonic Schrödinger equations, respectively. The lack of controllability on the half-line contrasts with the corresponding dynamics on a finite interval for a similar regularity setting. Our proof is based on an argument that uses the sharp fractional time trace estimates for solutions of the adjoint models. We also make several remarks on the connection of controllability and temporal regularity of spatial traces.
dc.identifier.doi10.1093/imamci/dnad032
dc.identifier.eissn1471-6887
dc.identifier.issn0265-0754
dc.identifier.urihttps://hdl.handle.net/11693/114457
dc.language.isoen_US
dc.publisherOxford University Press
dc.relation.isversionofhttps://dx.doi.org/10.1093/imamci/dnad032
dc.source.titleIMA Journal of Mathematical Control and Information
dc.subjectFokas method
dc.subjectSchrödinger equation
dc.subjectBiharmonic Schrödinger equation
dc.subjectControllability
dc.titleExistence of unattainable states for Schrödinger type flows on the half-line
dc.typeArticle

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