dc.creator | Cindea, Nicolae | es |
dc.creator | Fernández Cara, Enrique | es |
dc.creator | Münch, Arnaud | es |
dc.date.accessioned | 2016-07-04T12:04:18Z | |
dc.date.available | 2016-07-04T12:04:18Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Cindea, N., Fernández Cara, E. y Münch, A. (2013). Numerical controllability of the wave equation through primal methods and Carleman estimates. ESAIM: Control, Optimisation and Calculus of Variations, 19, 1076-1108. | |
dc.identifier.issn | 1292-8119 | es |
dc.identifier.issn | 1262-3377 | es |
dc.identifier.uri | http://hdl.handle.net/11441/43112 | |
dc.description.abstract | This paper deals with the numerical computation of boundary null controls for the 1D wave
equation with a potential. The goal is to compute approximations of controls that drive the solution
from a prescribed initial state to zero at a large enough controllability time. We do not apply in this
work the usual duality arguments but explore instead a direct approach in the framework of global
Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible
null controls a functional involving weighted integrals of the state and the control. The optimality
conditions show that both the optimal control and the associated state are expressed in terms of a
new variable, the solution of a fourth-order elliptic problem defined in the space-time domain. We
first prove that, for some specific weights determined by the global Carleman inequalities for the wave
equation, this problem is well-posed. Then, in the framework of the finite element method, we introduce
a family of finite-dimensional approximate control problems and we prove a strong convergence result.
Numerical experiments confirm the analysis. We complete our study with several comments. | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | EDP Sciences | es |
dc.relation.ispartof | ESAIM: Control, Optimisation and Calculus of Variations, 19, 1076-1108. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | one-dimensional wave equation | es |
dc.subject | null controllability | es |
dc.subject | finite element methods | es |
dc.subject | Carleman estimates | es |
dc.title | Numerical controllability of the wave equation through primal methods and Carleman estimates | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.publisherversion | http://www.esaim-cocv.org/articles/cocv/pdf/2013/04/cocv130046.pdf | |
dc.identifier.doi | 10.1051/cocv/2013046 | es |
dc.contributor.group | Universidad de Sevilla. FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software | es |
idus.format.extent | 33 p. | es |
dc.journaltitle | ESAIM: Control, Optimisation and Calculus of Variations | es |
dc.publication.volumen | 19 | es |
dc.publication.initialPage | 1076 | es |
dc.publication.endPage | 1108 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/43112 | |