# American Institute of Mathematical Sciences

September  2013, 2(3): 441-459. doi: 10.3934/eect.2013.2.441

## Carleman Estimates and null controllability of coupled degenerate systems

 1 Département de Mathématiques, Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC), Université Cadi Ayyad, Marrakech, 40000, B.P. 2390,, Morocco 2 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 25030 Besançon Cedex, France 3 Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Labo. MISI, Université Hassan 1er Settat 26000, B.P. 577, Morocco 4 Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco

Received  May 2012 Revised  June 2013 Published  July 2013

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].
Citation: El Mustapha Ait Ben Hassi, Farid Ammar khodja, Abdelkarim Hajjaj, Lahcen Maniar. Carleman Estimates and null controllability of coupled degenerate systems. Evolution Equations & Control Theory, 2013, 2 (3) : 441-459. doi: 10.3934/eect.2013.2.441
##### References:

show all references

##### References:
 [1] Brahim Allal, Abdelkarim Hajjaj, Lahcen Maniar, Jawad Salhi. Null controllability for singular cascade systems of $n$-coupled degenerate parabolic equations by one control force. Evolution Equations & Control Theory, 2021, 10 (3) : 545-573. doi: 10.3934/eect.2020080 [2] R. Demarque, J. Límaco, L. Viana. Local null controllability of coupled degenerate systems with nonlocal terms and one control force. Evolution Equations & Control Theory, 2020, 9 (3) : 605-634. doi: 10.3934/eect.2020026 [3] Genni Fragnelli. Null controllability of degenerate parabolic equations in non divergence form via Carleman estimates. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 687-701. doi: 10.3934/dcdss.2013.6.687 [4] J. Carmelo Flores, Luz De Teresa. Null controllability of one dimensional degenerate parabolic equations with first order terms. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3963-3981. doi: 10.3934/dcdsb.2020136 [5] Assia Benabdallah, Michel Cristofol, Patricia Gaitan, Luz de Teresa. Controllability to trajectories for some parabolic systems of three and two equations by one control force. Mathematical Control & Related Fields, 2014, 4 (1) : 17-44. doi: 10.3934/mcrf.2014.4.17 [6] Lingyang Liu, Xu Liu. Controllability and observability of some coupled stochastic parabolic systems. Mathematical Control & Related Fields, 2018, 8 (3&4) : 829-854. doi: 10.3934/mcrf.2018037 [7] Ait Ben Hassi El Mustapha, Fadili Mohamed, Maniar Lahcen. On Algebraic condition for null controllability of some coupled degenerate systems. Mathematical Control & Related Fields, 2019, 9 (1) : 77-95. doi: 10.3934/mcrf.2019004 [8] Kuntal Bhandari, Franck Boyer. Boundary null-controllability of coupled parabolic systems with Robin conditions. Evolution Equations & Control Theory, 2021, 10 (1) : 61-102. doi: 10.3934/eect.2020052 [9] Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. Null controllability of degenerate parabolic operators with drift. Networks & Heterogeneous Media, 2007, 2 (4) : 695-715. doi: 10.3934/nhm.2007.2.695 [10] Farid Ammar Khodja, Cherif Bouzidi, Cédric Dupaix, Lahcen Maniar. Null controllability of retarded parabolic equations. Mathematical Control & Related Fields, 2014, 4 (1) : 1-15. doi: 10.3934/mcrf.2014.4.1 [11] Brahim Allal, Abdelkarim Hajjaj, Jawad Salhi, Amine Sbai. Boundary controllability for a coupled system of degenerate/singular parabolic equations. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021055 [12] Morteza Fotouhi, Leila Salimi. Controllability results for a class of one dimensional degenerate/singular parabolic equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1415-1430. doi: 10.3934/cpaa.2013.12.1415 [13] Damien Allonsius, Franck Boyer. Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries. Mathematical Control & Related Fields, 2020, 10 (2) : 217-256. doi: 10.3934/mcrf.2019037 [14] Farid Ammar Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems. Mathematical Control & Related Fields, 2016, 6 (2) : 185-216. doi: 10.3934/mcrf.2016001 [15] Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations & Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020 [16] Lydia Ouaili. Minimal time of null controllability of two parabolic equations. Mathematical Control & Related Fields, 2020, 10 (1) : 89-112. doi: 10.3934/mcrf.2019031 [17] Ali Wehbe, Marwa Koumaiha, Layla Toufaily. Boundary observability and exact controllability of strongly coupled wave equations. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021091 [18] Larbi Berrahmoune. Null controllability for distributed systems with time-varying constraint and applications to parabolic-like equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3275-3303. doi: 10.3934/dcdsb.2020062 [19] Brahim Allal, Abdelkarim Hajjaj, Lahcen Maniar, Jawad Salhi. Lipschitz stability for some coupled degenerate parabolic systems with locally distributed observations of one component. Mathematical Control & Related Fields, 2020, 10 (3) : 643-667. doi: 10.3934/mcrf.2020014 [20] Fengyan Yang. Exact boundary null controllability for a coupled system of plate equations with variable coefficients. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021036

2020 Impact Factor: 1.081