Energy decay for the modified Kawahara equation posed in a bounded domain

Studied here is the eventual dissipation of solutions to initial–boundary value problems for the modified Kawahara equation with and without a localized damping term included. It is shown that solutions of undamped problems posed on a bounded interval may not decay if the length of the interval is c...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-01, Vol.385 (2), p.743-756
Main Authors: Araruna, F.D., Capistrano-Filho, R.A., Doronin, G.G.
Format: Article
Language:English
Subjects:
Critical set
Energy decay
Kawaharaʼs equation
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Summary:Studied here is the eventual dissipation of solutions to initial–boundary value problems for the modified Kawahara equation with and without a localized damping term included. It is shown that solutions of undamped problems posed on a bounded interval may not decay if the length of the interval is critical. In contrast, the energy associated to the locally damped problems is shown to be exponentially decreased independently of the interval length.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.07.003