# 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

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topVasconcellos, 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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