scholarly journals Null controllability for singular cascade systems of \begin{document}$ n $\end{document}-coupled degenerate parabolic equations by one control force

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Brahim Allal ◽  
◽  
Abdelkarim Hajjaj ◽  
Lahcen Maniar ◽  
Jawad Salhi ◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Null Controllability ◽  
Degenerate Parabolic Equations ◽  
Control Force ◽  
Cascade Systems ◽  
Degenerate Parabolic

Null controllability of a coupled degenerate system with the first and zero order terms by a single control

2020 ◽  
Vol 26 ◽  
pp. 107
Author(s):  
Bin Wu ◽  
Qun Chen ◽  
Tingchun Wang ◽  
Zewen Wang
Keyword(s):  
Adjoint System ◽  
Zero Order ◽  
Null Controllability ◽  
Carleman Estimate ◽  
Degenerate Parabolic Equations ◽  
Degenerate System ◽  
Control Force ◽  
Negative Order ◽  
Degenerate Parabolic ◽  
Linear Degenerate

This paper concerns the null controllability of a system of m linear degenerate parabolic equations with coupling terms of first and zero order, and only one control force localized in some arbitrary nonempty open subset ω of Ω. The key ingredient for proving the null controllability is to obtain the observability inequality for the corresponding adjoint system. Due to the degeneracy, we transfer to study an approximate nondegenerate adjoint system. In order to deal with the coupling first order terms, we first prove a new Carleman estimate for a degenerate parabolic equation in Sobolev spaces of negative order. Based on this Carleman estimate, we obtain a uniform Carleman estimate and then an observation inequality for this approximate adjoint system.

scholarly journals Null controllability of degenerate parabolic equations

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1061601-1061602
Author(s):  
Patrick Martinez ◽  
Piermaco Cannarsa ◽  
Judith Vancostenoble
Keyword(s):  
Parabolic Equations ◽  
Null Controllability ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic
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