Dans cette Note on étudie un problème d'atteignabilité pour une équation intégro-différentielle du second ordre par une approche utilisant des techniques d'analyse harmonique.
In this Note we analyze a reachability problem for an integro-differential equation by using a harmonic analysis approach.
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@article{CRMATH_2009__347_19-20_1153_0, author = {Loreti, Paola and Sforza, Daniela}, title = {Exact reachability for second-order integro-differential equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {1153--1158}, publisher = {Elsevier}, volume = {347}, number = {19-20}, year = {2009}, doi = {10.1016/j.crma.2009.08.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.08.007/} }
TY - JOUR AU - Loreti, Paola AU - Sforza, Daniela TI - Exact reachability for second-order integro-differential equations JO - Comptes Rendus. Mathématique PY - 2009 SP - 1153 EP - 1158 VL - 347 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.08.007/ DO - 10.1016/j.crma.2009.08.007 LA - en ID - CRMATH_2009__347_19-20_1153_0 ER -
%0 Journal Article %A Loreti, Paola %A Sforza, Daniela %T Exact reachability for second-order integro-differential equations %J Comptes Rendus. Mathématique %D 2009 %P 1153-1158 %V 347 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.08.007/ %R 10.1016/j.crma.2009.08.007 %G en %F CRMATH_2009__347_19-20_1153_0
Loreti, Paola; Sforza, Daniela. Exact reachability for second-order integro-differential equations. Comptes Rendus. Mathématique, Tome 347 (2009) no. 19-20, pp. 1153-1158. doi : 10.1016/j.crma.2009.08.007. http://www.numdam.org/articles/10.1016/j.crma.2009.08.007/
[1] Ingham-type inequalities for complex frequencies and applications to control theory, J. Math. Anal. Appl., Volume 324 (2006), pp. 941-954
[2] Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., Volume 68 (1989), pp. 457-465
[3] Some trigonometrical inequalities with applications to the theory of series, Math. Z., Volume 41 (1936), pp. 367-379
[4] Ingham type theorems for vector-valued functions and observability of coupled linear system, SIAM J. Control Optim., Volume 37 (1998), pp. 461-485
[5] Exact boundary controllability of an integro-differential equation, Appl. Math. Optim. (1987), pp. 223-250
[6] Boundary controllability of a viscoelastic string (Da Prato, G.; Iannelli, M., eds.), Volterra Integrodifferential Equations in Banach Spaces and Applications, Longman Sci. Tech., Harlow, Essex, 1989, pp. 258-270
[7] Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte, Recherches en Mathématiques Appliquées, vol. 8, Masson, Paris, 1988 (with appendices by E. Zuazua, C. Bardos, G. Lebeau and J. Rauch)
[8] Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 2. Perturbations, Recherches en Mathématiques Appliquées, vol. 9, Masson, Paris, 1988
[9] P. Loreti, D. Sforza, Reachability problems for a class of integro-differential equations, J. Differential Equations, in press
[10] Partial exact controllability for spherical membranes, SIAM J. Control Optim., Volume 35 (1997), pp. 641-653
[11] Evolutionary Integral Equations and Applications, Monographs in Mathematics, vol. 87, Birkhäuser Verlag, Basel, 1993
[12] Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., Volume 20 (1978), pp. 639-739
[13] Polynomial decay and control of a model for fluid–structure interaction, C. R. Math. Acad. Sci. Paris, Volume 336 (2003), pp. 745-750
[14] Polynomial decay and control of a hyperbolic–parabolic coupled system, J. Differential Equations, Volume 204 (2004), pp. 380-438
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