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Mathematical Control and Related Fields (MCRF)
 

Null controllability of retarded parabolic equations
Pages: 1 - 15, Issue 1, March 2014

doi:10.3934/mcrf.2014.4.1      Abstract        References        Full text (396.3K)           Related Articles

Farid Ammar Khodja - Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, F25030 Besançon Cedex, France (email)
Cherif Bouzidi - École Nationale Supérieure des Travaux Publics, Rue Sidi Garidi, BP 32, 16051 Alger, Algeria (email)
Cédric Dupaix - Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, F25030 Besançon Cedex, France (email)
Lahcen Maniar - Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco (email)

1 F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems, J. Evol. Equ., 9 (2009), 267-291. Available from: http://hal.archives-ouvertes.fr/hal-00290867/fr/.       
2 F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, Controllability for a class of reaction-diffusion systems: The generalized Kalman's condition, C. R. Math. Acad. Sci. Paris, 345 (2007), 543-548.       
3 F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, Differ. Equ. Appl., 1 (2009), 427-457.       
4 F. Ammar-Khodja, A. Benabdallah, M. González-Burgos and L. de Teresa, The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials, J. Math. Pures Appl. (9), 96 (2011), 555-590. Available from: http://hal.archives-ouvertes.fr/hal-00539825/fr/.       
5 M. Artola, Sur les perturbations des équations d'évolution: Application à des problèmes avec retard, Ann. Sci. École Norm. Sup. (4), 2 (1969), 137-253.       
6 V. Barbu, Exact controllability of the superlinear heat equation, Appl. Math. Optim., 42 (2000), 73-89.       
7 R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, 21, Springer-Verlag, New York, 1995.       
8 E. Fernández-Cara, M. González-Burgos and L. de Teresa, Boundary controllability of parabolic coupled equations, J. Funct. Anal., 259 (2010), 1720-1758.       
9 E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 17 (2000), 583-616.       
10 A. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, Korea, 1996.       
11 S.-I. Nakagiri, Optimal control of linear retarded systems in Banach spaces, J. Math. Anal. and Appl., 120 (1986), 169-210.       
12 S.-I. Nakagiri and M. Yamamoto, Controllability and observability of linear retarded systems in Banach spaces, Int. J. Control, 49 (1989), 1489-1504.       
13 J. Zabczyk, Mathematical Control Theory: An Introduction, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 1992.       

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