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dc.contributor.authorGueye, Mamadou
HAL ID: 174100
dc.contributor.authorLissy, Pierre
dc.date.accessioned2017-11-30T13:38:28Z
dc.date.available2017-11-30T13:38:28Z
dc.date.issued2016
dc.identifier.issn1262-3377
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17124
dc.language.isoenen
dc.subjectDegenerate parabolic equation
dc.subjectcost of the control
dc.subjectuniform controllability
dc.subjectBessel functions
dc.subject.ddc515en
dc.titleSingular Optimal Control of a 1-D Parabolic-Hyperbolic Degenerate Equation
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we consider the controllability of a strongly degenerate parabolic equation with a degenerate one-order transport term. Despite the strong degeneracy, we prove a result of well-posedness and null controllability with a Dirichlet boundary control that acts on the degenerate part of the boundary. Then, we study the uniform controllability in the vanishing viscosity limit and prove that the cost of the control explodes exponentially fast in small time and converges exponentially fast in large time in some adapted weighted norm. The main tools used are a spectral decomposition involving Bessel functions and their zeros, some usual results on admissibility of scalar controls for diagonal semigroups, and the moment method of Fattorini and Russell. Keywords: degenerate parabolic equations, cost of the control, uniform controllability, degenerate transport equation.
dc.relation.isversionofjnlnameESAIM: Control, Optimisation and Calculus of Variations
dc.relation.isversionofjnlvol22
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1184 - 1203
dc.relation.isversionofdoi10.1051/cocv/2016036
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewednon
dc.date.updated2017-12-19T10:42:36Z


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