Volume 49, Issue 2
On the Benjamin-Bona-Mahony Equation with a Localized Damping

Lionel Rosier

J. Math. Study, 49 (2016), pp. 195-204.

Published online: 2016-07

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  • Abstract

We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global well-posedness of the system and the convergence towards a solution of the BBM equation which is null on a band. If the Unique Continuation Property holds for the BBM equation, this implies that the origin is asymptotically stable for the damped BBM equation.

  • Keywords

Benjamin-Bona-Mahony equation, unique continuation property, internal stabilization, boundary stabilization.

  • AMS Subject Headings

35Q53, 93B05, 93D15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Lionel.Rosier@mines-paristech.fr (Lionel Rosier)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-195, author = {Lionel and Rosier and Lionel.Rosier@mines-paristech.fr and 13321 and Centre Automatique et Syst`emes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 06, France and Lionel Rosier}, title = {On the Benjamin-Bona-Mahony Equation with a Localized Damping}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {2}, pages = {195--204}, abstract = {

We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global well-posedness of the system and the convergence towards a solution of the BBM equation which is null on a band. If the Unique Continuation Property holds for the BBM equation, this implies that the origin is asymptotically stable for the damped BBM equation.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n2.16.06}, url = {http://global-sci.org/intro/article_detail/jms/998.html} }
TY - JOUR T1 - On the Benjamin-Bona-Mahony Equation with a Localized Damping AU - Rosier , Lionel JO - Journal of Mathematical Study VL - 2 SP - 195 EP - 204 PY - 2016 DA - 2016/07 SN - 49 DO - http://doi.org/10.4208/jms.v49n2.16.06 UR - https://global-sci.org/intro/article_detail/jms/998.html KW - Benjamin-Bona-Mahony equation, unique continuation property, internal stabilization, boundary stabilization. AB -

We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global well-posedness of the system and the convergence towards a solution of the BBM equation which is null on a band. If the Unique Continuation Property holds for the BBM equation, this implies that the origin is asymptotically stable for the damped BBM equation.

Lionel Rosier. (2019). On the Benjamin-Bona-Mahony Equation with a Localized Damping. Journal of Mathematical Study. 49 (2). 195-204. doi:10.4208/jms.v49n2.16.06
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