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

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

Year:    2016

Author:    Lionel Rosier

Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 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 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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 195–204

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

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

Author Details

Lionel Rosier

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