Partial Differential Equations/Optimal Control
Exact reachability for second-order integro-differential equations
[Atteignabilité exacte pour des équations intégro-différentielles du deuxième ordre]
Comptes Rendus. Mathématique, Tome 347 (2009) no. 19-20, pp. 1153-1158.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.08.007
Loreti, Paola 1 ; Sforza, Daniela 1

1 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161 Roma, Italy
@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] Edward, J. Ingham-type inequalities for complex frequencies and applications to control theory, J. Math. Anal. Appl., Volume 324 (2006), pp. 941-954

[2] Haraux, A. Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., Volume 68 (1989), pp. 457-465

[3] Ingham, A.E. Some trigonometrical inequalities with applications to the theory of series, Math. Z., Volume 41 (1936), pp. 367-379

[4] Komornik, V.; Loreti, P. Ingham type theorems for vector-valued functions and observability of coupled linear system, SIAM J. Control Optim., Volume 37 (1998), pp. 461-485

[5] Leugering, G. Exact boundary controllability of an integro-differential equation, Appl. Math. Optim. (1987), pp. 223-250

[6] Leugering, G. 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] Lions, J.-L. 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] Lions, J.-L. 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] Loreti, P.; Valente, V. Partial exact controllability for spherical membranes, SIAM J. Control Optim., Volume 35 (1997), pp. 641-653

[11] Prüss, J. Evolutionary Integral Equations and Applications, Monographs in Mathematics, vol. 87, Birkhäuser Verlag, Basel, 1993

[12] Russell, D.L. Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., Volume 20 (1978), pp. 639-739

[13] Zhang, X.; Zuazua, E. Polynomial decay and control of a 1d model for fluid–structure interaction, C. R. Math. Acad. Sci. Paris, Volume 336 (2003), pp. 745-750

[14] Zhang, X.; Zuazua, E. Polynomial decay and control of a 1d hyperbolic–parabolic coupled system, J. Differential Equations, Volume 204 (2004), pp. 380-438

Cité par Sources :