On the Benjamin-Bona-Mahony Equation with a Localized Damping
Author: Lionel Rosier, Journal of Mathematical Study, Vol 49 No 2, pp. 195 - 204, 2016. DOI: 10.4208/jms.v49n2.16.06
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.
BibTeX:
@Article{2017-06-28,
author = {Lionel Rosier},
title = {On the Benjamin-Bona-Mahony Equation with a Localized Damping},
journal = {Journal of Mathematical Study},
volume = {49},
number = {2},
pages = {195 - 204},
year = {2016},
}
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.
BibTeX:
@Article{2017-06-28,
author = {Lionel Rosier},
title = {On the Benjamin-Bona-Mahony Equation with a Localized Damping},
journal = {Journal of Mathematical Study},
volume = {49},
number = {2},
pages = {195 - 204},
year = {2016},
}