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Stabilization of the Kawahara equation with localized damping

Published online by Cambridge University Press:  30 October 2009

Carlos F. Vasconcellos
Affiliation:
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
Patricia N. da Silva
Affiliation:
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
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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