We consider abstract second order evolution equations with unbounded feedback with delay. Existence results are obtained under some realistic assumptions. Sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability. Some new examples that enter into our abstract framework are presented.
Mots-clés : second order evolution equations, wave equations, delay, stabilization functional
@article{COCV_2010__16_2_420_0,
author = {Nicaise, Serge and Valein, Julie},
title = {Stabilization of second order evolution equations with unbounded feedback with delay},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {420--456},
publisher = {EDP-Sciences},
volume = {16},
number = {2},
year = {2010},
doi = {10.1051/cocv/2009007},
mrnumber = {2654201},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2009007/}
}
TY - JOUR AU - Nicaise, Serge AU - Valein, Julie TI - Stabilization of second order evolution equations with unbounded feedback with delay JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 420 EP - 456 VL - 16 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2009007/ DO - 10.1051/cocv/2009007 LA - en ID - COCV_2010__16_2_420_0 ER -
%0 Journal Article %A Nicaise, Serge %A Valein, Julie %T Stabilization of second order evolution equations with unbounded feedback with delay %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 420-456 %V 16 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2009007/ %R 10.1051/cocv/2009007 %G en %F COCV_2010__16_2_420_0
Nicaise, Serge; Valein, Julie. Stabilization of second order evolution equations with unbounded feedback with delay. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 420-456. doi : 10.1051/cocv/2009007. https://www.numdam.org/articles/10.1051/cocv/2009007/
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