Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

dc.contributor.authorBiccari, Umberto
dc.date.accessioned2024-12-12T10:40:31Z
dc.date.available2024-12-12T10:40:31Z
dc.date.issued2022-02
dc.date.updated2024-12-12T10:40:31Z
dc.description.abstractWe analyze the interior controllability problem for a non-local Schrödinger equation involving the fractional Laplace operator (-Δ)s, s ϵ(0 1), on a bounded C1 1 domain  RN. We first consider the problem in one space dimension and employ spectral techniques to prove that, for s ϵ [1/2/1), null-controllability is achieved through an L2(ωX (0,T)) function acting in a subset ω Ω of the domain. This result is then extended to the multi-dimensional case by applying the classical multiplier method, joint with a Pohozaev-type identity for the fractional Laplacian.en
dc.description.sponsorshipThis project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon). This work was partially supported by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), by the Elkartek grant KK-2020/00091 CONVADP of the Basque government and by the Grant FA9550-18-1-0242 of AFOSRen
dc.identifier.citationBiccari, U. (2022). Internal control for a non-local Schrödinger equation involving the fractional Laplace operator. Evolution Equations and Control Theory, 11(1), 301-324. https://doi.org/10.3934/EECT.2021014
dc.identifier.doi10.3934/EECT.2021014
dc.identifier.eissn2163-2480
dc.identifier.issn2163-2472
dc.identifier.urihttp://hdl.handle.net/20.500.14454/2164
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.subject.otherFractional Laplacian
dc.subject.otherSchrödinger equation
dc.subject.otherControllability
dc.subject.otherPohozaev identity
dc.titleInternal control for a non-local Schrödinger equation involving the fractional Laplace operatoren
dc.typejournal article
dcterms.accessRightsmetadata only access
oaire.citation.endPage324
oaire.citation.issue1
oaire.citation.startPage301
oaire.citation.titleEvolution Equations and Control Theory
oaire.citation.volume11
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