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dc.contributor.authorBiccari, U.
dc.date.accessioned2016-06-13T13:33:49Z
dc.date.available2016-06-13T13:33:49Z
dc.date.issued2014-12-31
dc.identifier.issn0363-0129
dc.identifier.urihttp://hdl.handle.net/20.500.11824/235
dc.description.abstractWe analyse the interior controllability problem for a non-local Schr\"odinger equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability from a neighbourhood of the boundary of the domain is obtained for exponents $s$ in the interval $[1/2,1)$, while for $s<1/2$ the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a non-local wave equation involving the higher order fractional Laplace operator $(-\Delta)^{2s}=(-\Delta)^s(-\Delta)^s$, $s\in[1/2,1)$. The results follow from a new Pohozaev-type identity for the fractional Laplacian recently proved by X. Ros-Oton and J. Serra and from an explicit computation of the spectrum of the operator in the one dimensional case.
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dc.language.isoengen_US
dc.publisher
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleInternal control for non-local Schrodinger and wave equations involving the fractional Laplace operator
dc.typeinfo:eu-repo/semantics/articleen_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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