On the Benjamin-Bona-Mahony Equation with a Localized Damping

Journal of Mathematical Study
Vol. 49 No. 2 (2016), pp. 195-204
DOI: 10.4208/jms.v49n2.16.06
Preview Buy Article Full text requires purchase or subscription
Author(s)
    Lionel Rosier
    Centre Automatique et Syst`emes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 06, France
    Search all author publications
Centre Automatique et Syst`emes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 06, France
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.
More from this issue
Preface
pp. 0-0
Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory
Brauner
pp. 93-110
New Results for the BBM Equation
Chen
pp. 111-131
Existence and Stability of Solitary Waves of an M-Coupled Nonlinear Schrödinger System
Liu et al.
pp. 132-148
Stay updated
Share
How to Cite
RIS BibTeX