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dc.contributor.authorLissy, Pierre
dc.date.accessioned2017-03-18T10:26:32Z
dc.date.available2017-03-18T10:26:32Z
dc.date.issued2015
dc.identifier.issn0022-0396
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16387
dc.language.isoenen
dc.subjectlinear equations of parabolic or dispersive typeen
dc.subject.ddc515en
dc.titleExplicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport–diffusion equationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional Laplace operator. We notably deduce the following striking result: in the case of the heat equation controlled on the boundary, Miller's conjecture formulated in Miller (2004) [16] is not verified. Moreover, we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one-dimensional convection–diffusion equation with negative speed controlled on the left boundary, proving that the conjecture formulated in Coron and Guerrero (2005) [2] concerning this problem is also not verified at least for negative speeds.The proof is based on complex analysis, and more precisely on a representation formula for entire functions of exponential type, and is quite related to the moment method.en
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol259en
dc.relation.isversionofjnlissue10en
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages5331-5352en
dc.relation.isversionofdoi10.1016/j.jde.2015.06.031en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01133526en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-10T13:44:12Z
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