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

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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 : 10.1051/cocv/2009041
Classification : 35Q35, 35B40, 35Q53
Keywords: Kawahara equation, stabilization, energy decay, localized damping 
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     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},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {1},
     year = {2011},
     doi = {10.1051/cocv/2009041},
     mrnumber = {2775188},
     zbl = {1210.35215},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009041/}
}
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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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