Volume 49, Issue 2
On the Benjamin-Bona-Mahony Equation with a Localized Damping

Lionel Rosier

10.4208/jms.v49n2.16.06

J. Math. Study, 49 (2016), pp. 195-204.

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  • 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 wellposedness 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.

  • History

Published online: 2016-07

  • AMS Subject Headings

35Q53, 93B05, 93D15

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