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

Preview Full PDF 2 539
Export citation
  • 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 wellposedness 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)

  • References
  • Hide All
    View All

@Article{JMS-49-195, author = {Rosier , Lionel }, 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 wellposedness 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} }
Copy to clipboard
The citation has been copied to your clipboard