Internal control for a non-local Schrödinger equation involving the fractional Laplace operator
dc.contributor.author | Biccari, Umberto | |
dc.date.accessioned | 2024-12-12T10:40:31Z | |
dc.date.available | 2024-12-12T10:40:31Z | |
dc.date.issued | 2022-02 | |
dc.date.updated | 2024-12-12T10:40:31Z | |
dc.description.abstract | We 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.sponsorship | This 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 AFOSR | en |
dc.identifier.citation | Biccari, 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.doi | 10.3934/EECT.2021014 | |
dc.identifier.eissn | 2163-2480 | |
dc.identifier.issn | 2163-2472 | |
dc.identifier.uri | http://hdl.handle.net/20.500.14454/2164 | |
dc.language.iso | eng | |
dc.publisher | American Institute of Mathematical Sciences | |
dc.subject.other | Fractional Laplacian | |
dc.subject.other | Schrödinger equation | |
dc.subject.other | Controllability | |
dc.subject.other | Pohozaev identity | |
dc.title | Internal control for a non-local Schrödinger equation involving the fractional Laplace operator | en |
dc.type | journal article | |
dcterms.accessRights | metadata only access | |
oaire.citation.endPage | 324 | |
oaire.citation.issue | 1 | |
oaire.citation.startPage | 301 | |
oaire.citation.title | Evolution Equations and Control Theory | |
oaire.citation.volume | 11 |