On the Benjamin-Bona-Mahony equation with a localized damping

2016/05/31 by Lionel Rosier, Rosier, Lionel
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1605.09574

openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 asymp-totically stable for the damped BBM equation.

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