We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical for the contribution of low frequencies when the damping is effective at infinity. On the other hand, the usual Geometric Control Condition is not necessarily satisfied so we may have a loss of regularity for the contribution of high frequencies. Since our results are new even in the Euclidean space, we also state a similar result in this case.
Mots-clés : Local and global energy decay, dissipative wave equation, wave guides, diffusive phenomenon, semiclassical analysis, low frequency resolvent estimates
@article{COCV_2018__24_2_519_0,
author = {Malloug, Mohamed and Royer, Julien},
title = {Energy decay in a wave guide with dissipation at infinity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {519--549},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017054},
mrnumber = {3816403},
zbl = {1409.35032},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2017054/}
}
TY - JOUR AU - Malloug, Mohamed AU - Royer, Julien TI - Energy decay in a wave guide with dissipation at infinity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 519 EP - 549 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017054/ DO - 10.1051/cocv/2017054 LA - en ID - COCV_2018__24_2_519_0 ER -
%0 Journal Article %A Malloug, Mohamed %A Royer, Julien %T Energy decay in a wave guide with dissipation at infinity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 519-549 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017054/ %R 10.1051/cocv/2017054 %G en %F COCV_2018__24_2_519_0
Malloug, Mohamed; Royer, Julien. Energy decay in a wave guide with dissipation at infinity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 519-549. doi : 10.1051/cocv/2017054. http://archive.numdam.org/articles/10.1051/cocv/2017054/
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