Evolution Equations and Control Theory (EECT)

Carleman Estimates and null controllability of coupled degenerate systems

Pages: 441 - 459, Volume 2, Issue 3, September 2013      doi:10.3934/eect.2013.2.441

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El Mustapha Ait Ben Hassi - Département de Mathématiques, Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC), Université Cadi Ayyad, Marrakech, 40000, B.P. 2390,, Morocco (email)
Farid Ammar khodja - Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 25030 Besançon Cedex, France (email)
Abdelkarim Hajjaj - Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Labo. MISI, Université Hassan 1er Settat 26000, B.P. 577, Morocco (email)
Lahcen Maniar - Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco (email)

Abstract: In this paper, we study the null controllability of weakly degenerate parabolic systems with two different diffusion coefficients and one control force. To obtain this aim, we had to develop new global Carleman estimates for a degenerate parabolic equation, with weight functions different from the ones of [2], [10] and [31].

Keywords:  Carleman estimates, degenerate, parabolic equations, coupled systems, one control force, observability inequality, null controllability, semigroups.
Mathematics Subject Classification:  35K05, 35K65, 47D06, 93C20.

Received: May 2012;      Revised: June 2013;      Available Online: July 2013.