Electron. J. Differential Equations, Vol. 2016 (2016), No. 305, pp. 1-22.

Null controllability for linear parabolic cascade systems with interior degeneracy

Idriss Boutaayamou, Jawad Salhi

We study the null controllability problem for linear degenerate parabolic systems with one control force through Carleman estimates for the associated adjoint problem. The novelty of this article is that for the first time it is considered a problem with an interior degeneracy and a control set that only requires to contain an interval lying on one side of the degeneracy points. The obtained result improves and complements a number of earlier works. As a consequence, observability inequalities are established.

Submitted October 14, 2016. Published November 30, 2016.
Math Subject Classifications: 35K65, 35K40, 35B45, 93B05, 93B07.
Key Words: Degenerate parabolic systems; interior degeneracy; one control force; Carleman estimates, observability inequalities; null controllability.

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Idriss Boutaayamou
Département de Mathématiques Informatiques et Gestion
Faculté Polydisciplinaires de Ouarzazate
Université Ibn Zohr
B.P. 638, Ouarzazate 45000, Morocco
email: dsboutaayamou@gmail.com
Jawad Salhi
Faculté des Sciences et Techniques
Université Hassan 1er, Laboratoire MISI
B.P. 577, Settat 26000, Morocco
email: sj.salhi@gmail.com

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