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energy decay

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Stabilization of the Kawahara equationwith localized damping
Carlos F. Vasconcellos, Patricia N. da Silva
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 1 / January 2011

Published online by Cambridge University Press:

30 October 2009, pp. 102-116

Print publication:

January 2011
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We study the stabilization of global solutions of theKawahara (K) equation in a bounded interval, under the effect ofa localized damping mechanism. The Kawahara equation is a modelfor small amplitude long waves. Using multiplier techniques andcompactness arguments we prove the exponential decay of the solutions of the (K) model. The proofrequires of a unique continuation theorem and the smoothing effectof the (K) equation on the real line, which are proved in this work.