We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
Keywords: Kawahara equation, stabilization, energy decay, localized damping
@article{COCV_2011__17_1_102_0,
author = {Vasconcellos, Carlos F. and da Silva, Patricia N.},
title = {Stabilization of the {Kawahara} equation with localized damping},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {102--116},
year = {2011},
publisher = {EDP Sciences},
volume = {17},
number = {1},
doi = {10.1051/cocv/2009041},
mrnumber = {2775188},
zbl = {1210.35215},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2009041/}
}
TY - JOUR AU - Vasconcellos, Carlos F. AU - da Silva, Patricia N. TI - Stabilization of the Kawahara equation with localized damping JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 102 EP - 116 VL - 17 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2009041/ DO - 10.1051/cocv/2009041 LA - en ID - COCV_2011__17_1_102_0 ER -
%0 Journal Article %A Vasconcellos, Carlos F. %A da Silva, Patricia N. %T Stabilization of the Kawahara equation with localized damping %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 102-116 %V 17 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2009041/ %R 10.1051/cocv/2009041 %G en %F COCV_2011__17_1_102_0
Vasconcellos, Carlos F.; da Silva, Patricia N. Stabilization of the Kawahara equation with localized damping. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 102-116. doi: 10.1051/cocv/2009041
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