Null controllability for singular cascade systems of $ n $-coupled degenerate parabolic equations by one control force

Brahim Allal; Abdelkarim Hajjaj; Lahcen Maniar; Jawad Salhi

doi:10.3934/eect.2020080

Article Contents

2021, Volume 10, Issue 3: 545-573. Doi: 10.3934/eect.2020080

This issue Previous Article Funnel control for boundary control systems Next Article On finite Morse index solutions of higher order fractional elliptic equations

Null controllability for singular cascade systems of $ n $-coupled degenerate parabolic equations by one control force

1.
Faculté des Sciences et Techniques, Université Hassan 1er, Laboratoire MISI, B.P. 577, Settat 26000, Morocco
2.
Département de Mathématiques, Faculté des Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC), Université Cadi Ayyad, Marrakech 40000, B.P. 2390, Morocco

^* Corresponding author: Lahcen Maniar
^* Corresponding author: Lahcen Maniar

Received: June 2019

Revised: March 2020

Early access: July 13, 2020

Published online: July 13, 2020

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Abstract

In this paper, we consider a class of cascade systems of $ n $-coupled degenerate parabolic equations with singular lower order terms. We assume that both degeneracy and singularity occur in the interior of the space domain and we focus on null controllability problem. To this aim, we prove first Carleman estimates for the associated adjoint problem, then, we infer from it an indirect observability inequality. As a consequence, we deduce null controllability result when a unique distributed control is exerted on the system.

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Mathematics Subject Classification: Primary: 35K65, 35K67, 93B05; Secondary: 93C20, 47D06.

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