| Issue |
ESAIM: COCV
Volume 17, Number 1, January-March 2011
|
|
|---|---|---|
| Page(s) | 102 - 116 | |
| DOI | https://doi.org/10.1051/cocv/2009041 | |
| Published online | 30 October 2009 | |
Stabilization of the Kawahara equation with localized damping
Instituto de Matemática e Estatística – UERJ,
524 R. São Francisco Xavier, Sala 6016, Bloco D –
CEP 20550-013, Rio de Janeiro, Brazil. cfredvasc@ime.uerj.br; nunes@ime.uerj.br
Received:
8
September
2008
Revised:
27
January
2009
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.
Mathematics Subject Classification: 35Q35 / 35B40 / 35Q53
Key words: Kawahara equation / stabilization / energy decay / localized damping
© EDP Sciences, SMAI, 2009
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