Electron. J. Differential Equations, Vol. 2016 (2016), No. 292, pp. 1-25.

Carleman estimates and null controllability of degenerate/singular parabolic systems

Abdelkarim Hajjaj, Lahcen Maniar, Jawad Salhi

Abstract:
We study null controllability properties for parabolic coupled systems with degeneracy and singularity occurring in the interior of the spatial domain. This article is the first to consider a problem with singular coupling terms; previous result cannot be adapted to this situation. In particular, we focus on the well posedness of the problem and then we prove Carleman estimates for the associated adjoint problem.

Submitted March 25, 2016. Published November 11, 2016.
Math Subject Classifications: 35K67, 35K65, 35K40, 35B45, 93B07, 93B05.
Key Words: Carleman estimates; singular degenerate equations; coupled systems; observability inequality; null controllability.

Show me the PDF file (343 KB), TEX file for this article.

Abdelkarim Hajjaj
Laboratoire MISI, FST
Univ. Hassan 1, B.P. 577
26000 Settat, Morocco
email: abdelkarim.hajjaj@uhp.ac.ma
Lahcen Maniar
Département de Mathématiques
Faculté des Sciences Semlalia
LMDP, UMMISCO (IRD-UPMC), Université Cadi Ayyad
Marrakech 40000, B.P. 2390, Morocco
email: maniar@uca.ma, lahcenmaniar@gmail.com
Jawad Salhi
Laboratoire MISI, FST
Univ. Hassan 1, B.P. 577
26000 Settat, Morocco
email: sj.salhi@gmail.com

Return to the EJDE web page