We study the strong stabilization of wave equations on some sphere-like manifolds, with rough damping terms which do not satisfy the geometric control condition posed by Rauch−Taylor [J. Rauch and M. Taylor, Commun. Pure Appl. Math. 28 (1975) 501–523] and Bardos−Lebeau−Rauch [C. Bardos, G. Lebeau and J. Rauch, SIAM J. Control Optimiz. 30 (1992) 1024–1065]. We begin with an unpublished result of G. Lebeau, which states that on
Mots-clés : Wave equation, semiclassical analysis, control theory, geodesic flow
@article{COCV_2018__24_4_1759_0, author = {Zhu, Hui}, title = {Stabilization of damped waves on spheres and {Zoll} surfaces of revolution}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1759--1788}, publisher = {EDP-Sciences}, volume = {24}, number = {4}, year = {2018}, doi = {10.1051/cocv/2017073}, zbl = {1421.35032}, mrnumber = {3922432}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017073/} }
TY - JOUR AU - Zhu, Hui TI - Stabilization of damped waves on spheres and Zoll surfaces of revolution JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1759 EP - 1788 VL - 24 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017073/ DO - 10.1051/cocv/2017073 LA - en ID - COCV_2018__24_4_1759_0 ER -
%0 Journal Article %A Zhu, Hui %T Stabilization of damped waves on spheres and Zoll surfaces of revolution %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1759-1788 %V 24 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017073/ %R 10.1051/cocv/2017073 %G en %F COCV_2018__24_4_1759_0
Zhu, Hui. Stabilization of damped waves on spheres and Zoll surfaces of revolution. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1759-1788. doi : 10.1051/cocv/2017073. http://archive.numdam.org/articles/10.1051/cocv/2017073/
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