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.