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dc.contributor.authorChaves-Silva, F.W.
dc.contributor.authorRosier, L.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-06-13T13:33:48Z
dc.date.available2016-06-13T13:33:48Z
dc.date.issued2014-12-31
dc.identifier.issn0021-7824
dc.identifier.urihttp://hdl.handle.net/20.500.11824/212
dc.description.abstractIn this paper, we consider the wave equation with both viscous Kelvin-Voigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null controllability when the control region, driven by the flow of an ODE, covers all the domain. The proof is based upon the interpretation of the system as, roughly, the coupling of a heat equation with an ordinary differential equation (ODE). The presence of the ODE for which there is no propagation along the space variable makes the controllability of the system impossible when the control is confined into a subset in space that does not move. The null controllability of the system with a moving control is established in using the observability of the adjoint system and some Carleman estimates for a coupled system of a parabolic equation and an ODE with the same singular weight, adapted to the geometry of the moving support of the control. This extends to the multi-dimensional case the results by P. Martin et al. in the one-dimensional case, employing 1-d Fourier analysis techniques.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleNull controllability of a system of viscoelasticity with a moving control
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.matpur.2013.05.009
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S002178241300086X
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/246775en_US
dc.relation.projectIDES/6PN/MTM2011-29306-C02-01en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleJournal des Mathematiques Pures et Appliqueesen_US


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