Stabilization of the Kawahara equation with localized damping
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 1, p. 102-116

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.

DOI : https://doi.org/10.1051/cocv/2009041
Classification:  35Q35,  35B40,  35Q53
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},
publisher = {EDP-Sciences},
volume = {17},
number = {1},
year = {2011},
pages = {102-116},
doi = {10.1051/cocv/2009041},
zbl = {1210.35215},
mrnumber = {2775188},
language = {en},
url = {http://www.numdam.org/item/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, Volume 17 (2011) no. 1, pp. 102-116. doi : 10.1051/cocv/2009041. http://www.numdam.org/item/COCV_2011__17_1_102_0/

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