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dc.contributor.authorLissy, Pierre
dc.date.accessioned2020-04-29T11:21:33Z
dc.date.available2020-04-29T11:21:33Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20675
dc.language.isoenen
dc.subjectControllabilityen
dc.subjectobservabilityen
dc.subjectfractional parabolic equations,en
dc.subjectprolate spheroidalwave functionsen
dc.subject.ddc515en
dc.titleA non-controllability result for the half-heat equation on the whole line based on the prolate spheroidal wave functions and its application to the Grushin equationen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this article, we revisit a result by A. Koenig concerning the non-controllability of the half-heat equation posed on R, with a control domain that is an open set whose exterior contains an interval. The main novelty of the present article is to disprove the corresponding observability inequality by using as an initial condition a family of prolate spheroidal wave function (PSWF) translated in the Fourier space, associated to a parameter c that goes to ∞. The proof is essentially based on the dual nature of the PSWF together with direct computations, showing that the solution "does not spread out" too much during time. As a consequence, we obtain a new non-controllability result on the Grushin equation posed on R × R.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages20en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02420212en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2020-02
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-04-29T11:18:43Z
hal.person.labIds60


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