Comptes Rendus
no. 19-20
Partial Differential Equations/Optimal Control
Exact reachability for second-order integro-differential equations
[Atteignabilité exacte pour des équations intégro-différentielles du deuxième ordre]

Présenté par : Philippe G. Ciarlet

Paola Loreti1 ; Daniela Sforza1
1 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161 Roma, Italy
Comptes Rendus. Mathématique, Volume 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
Paola Loreti 1 ; Daniela Sforza 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 = {Paola Loreti and Daniela Sforza},
     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},
}
TY  - JOUR
AU  - Paola Loreti
AU  - Daniela Sforza
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
DO  - 10.1016/j.crma.2009.08.007
LA  - en
ID  - CRMATH_2009__347_19-20_1153_0
ER  - 
%0 Journal Article
%A Paola Loreti
%A Daniela Sforza
%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
%R 10.1016/j.crma.2009.08.007
%G en
%F CRMATH_2009__347_19-20_1153_0
Paola Loreti; Daniela Sforza. Exact reachability for second-order integro-differential equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1153-1158. doi : 10.1016/j.crma.2009.08.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.08.007/

[1] J. Edward Ingham-type inequalities for complex frequencies and applications to control theory, J. Math. Anal. Appl., Volume 324 (2006), pp. 941-954

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

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

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

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

[6] G. Leugering Boundary controllability of a viscoelastic string (G. Da Prato; M. Iannelli, eds.), Volterra Integrodifferential Equations in Banach Spaces and Applications, Longman Sci. Tech., Harlow, Essex, 1989, pp. 258-270

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

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

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

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

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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

On the exact controllability of a system of mixed order with essential spectrum

Farid Ammar-Khodja; Giuseppe Geymonat; Arnaud Münch

C. R. Math (2008)

An Ingham type proof for the boundary observability of a N−d wave equation

Michel Mehrenberger

C. R. Math (2009)