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 - <p style="text-align: justify;">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.</p>