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.
Mots-clés : Null controllability, degenerate parabolic system, Carleman estimate, observation inequality
@article{COCV_2020__26_1_A107_0,
author = {Wu, Bin and Chen, Qun and Wang, Tingchun and Wang, Zewen},
title = {Null controllability of a coupled degenerate system with the first and zero order terms by a single control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020042},
mrnumber = {4185052},
zbl = {1459.35240},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2020042/}
}
TY - JOUR AU - Wu, Bin AU - Chen, Qun AU - Wang, Tingchun AU - Wang, Zewen TI - Null controllability of a coupled degenerate system with the first and zero order terms by a single control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020042/ DO - 10.1051/cocv/2020042 LA - en ID - COCV_2020__26_1_A107_0 ER -
%0 Journal Article %A Wu, Bin %A Chen, Qun %A Wang, Tingchun %A Wang, Zewen %T Null controllability of a coupled degenerate system with the first and zero order terms by a single control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020042/ %R 10.1051/cocv/2020042 %G en %F COCV_2020__26_1_A107_0
Wu, Bin; Chen, Qun; Wang, Tingchun; Wang, Zewen. Null controllability of a coupled degenerate system with the first and zero order terms by a single control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 107. doi : 10.1051/cocv/2020042. http://www.numdam.org/articles/10.1051/cocv/2020042/
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