| dc.contributor.author | Lissy, Pierre | |
| dc.date.accessioned | 2017-03-18T10:26:32Z | |
| dc.date.available | 2017-03-18T10:26:32Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/16387 | |
| dc.language.iso | en | en |
| dc.subject | linear equations of parabolic or dispersive type | en |
| dc.subject.ddc | 515 | en |
| dc.title | Explicit 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 equation | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.description.abstracten | In 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.isversionofjnlname | Journal of Differential Equations | |
| dc.relation.isversionofjnlvol | 259 | en |
| dc.relation.isversionofjnlissue | 10 | en |
| dc.relation.isversionofjnldate | 2015 | |
| dc.relation.isversionofjnlpages | 5331-5352 | en |
| dc.relation.isversionofdoi | 10.1016/j.jde.2015.06.031 | en |
| dc.identifier.urlsite | https://hal.archives-ouvertes.fr/hal-01133526 | en |
| dc.relation.isversionofjnlpublisher | Elsevier | en |
| dc.subject.ddclabel | Analyse | en |
| dc.relation.forthcoming | non | en |
| dc.relation.forthcomingprint | non | en |
| dc.description.ssrncandidate | non | en |
| dc.description.halcandidate | non | en |
| dc.description.readership | recherche | en |
| dc.description.audience | International | en |
| dc.relation.Isversionofjnlpeerreviewed | oui | en |
| dc.relation.Isversionofjnlpeerreviewed | oui | en |
| dc.date.updated | 2017-03-10T13:44:12Z | |
| hal.person.labIds | | |
