Stabilization of the Kawahara equation with localized damping
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 1, pp. 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 : 10.1051/cocv/2009041
Classification : 35Q35, 35B40, 35Q53
Mots clés : Kawahara equation, stabilization, energy decay, localized damping
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     title = {Stabilization of the {Kawahara} equation with localized damping},
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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. http://archive.numdam.org/articles/10.1051/cocv/2009041/

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