Stabilization of the Kawahara equation with localized damping

Carlos F. Vasconcellos; Patricia N. da Silva

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 1, page 102-116
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Vasconcellos, Carlos F., and da Silva, Patricia N.. "Stabilization of the Kawahara equation with localized damping." ESAIM: Control, Optimisation and Calculus of Variations 17.1 (2011): 102-116. <http://eudml.org/doc/272879>.

@article{Vasconcellos2011,
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.},
author = {Vasconcellos, Carlos F., da Silva, Patricia N.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Kawahara equation; stabilization; energy decay; localized damping},
language = {eng},
number = {1},
pages = {102-116},
publisher = {EDP-Sciences},
title = {Stabilization of the Kawahara equation with localized damping},
url = {http://eudml.org/doc/272879},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Vasconcellos, Carlos F.
AU - da Silva, Patricia N.
TI - Stabilization of the Kawahara equation with localized damping
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 1
SP - 102
EP - 116
AB - 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.
LA - eng
KW - Kawahara equation; stabilization; energy decay; localized damping
UR - http://eudml.org/doc/272879
ER -

References

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