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

Authors

  • Lionel Rosier Centre Automatique et Syst`emes, MINES ParisTech, PSL Research University, 60 Boulevard Saint-Michel, 75272 Paris Cedex 06, France

DOI:

https://doi.org/10.4208/jms.v49n2.16.06

Keywords:

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

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.

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Published

2016-06-02

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Issue

Vol. 49 No. 2 (2016)

Section

Articles

How to Cite

On the Benjamin-Bona-Mahony Equation with a Localized Damping. (2016). Journal of Mathematical Study, 49(2), 195-204. https://doi.org/10.4208/jms.v49n2.16.06