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The cost of the control in the case of a minimal time of control: the example of the one-dimensional heat equation

dc.contributor.authorLissy, Pierre
dc.date.accessioned2017-11-30T13:31:47Z
dc.date.available2017-11-30T13:31:47Z
dc.date.issued2017
dc.identifier.issn0022-247X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17123
dc.language.isoenen
dc.subjectnon-harmonic Fourier series
dc.subjectminimal time
dc.subjectcontrollability cost
dc.subjectnull controllability
dc.subjectparabolic equations
dc.subjectmoment method
dc.subject.ddc515en
dc.titleThe cost of the control in the case of a minimal time of control: the example of the one-dimensional heat equation
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this article, we consider the controllability of the one-dimensional heat equation with an internal control depending only on the time variable and an imposed profile depending on the space variable. It is well-known that in this context, there might exist a minimal time of null-controllability T0, depending on the behavior of the Fourier coefficients of the profile. We prove two different results. The first one, which is surprising, is that the cost of the controllability in time T > T0 close to T0 may explode in an arbitrary way. On the other hand, we prove as a second result that for a large class of profiles, the cost of controllability at time T > T0 is bounded from above by exp(C(T0)/(T − T0)) for some constant C(T0) > 0 depending on T0. The main method used here is the moment method and some tools coming from complex analysis.
dc.relation.isversionofjnlnameJournal of Mathematical Analysis and Applications
dc.relation.isversionofjnlvol451
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages497-507
dc.relation.isversionofdoi10.1016/j.jmaa.2017.01.096
dc.relation.isversionofjnlpublisherAcademic Press
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T15:01:19Z


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