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Sierra Fonseca, Oscar A.; Pazoto, Ademir F.
Zeitschrift für angewandte Mathematik und Physik, 12/2022, Letnik: 73, Številka: 6Journal Article
The article deals with a class of Boussinesq system coupling two higher-order Benjamin–Bona–Mahony (BBM)-type equations. Introducing appropriate damping mechanisms, we study the asymptotic behavior in time of the corresponding damped models. This is done both in the case of internal and boundary damping. We first prove the global well-posedness of the systems and the convergence towards a solution which is null on a band. Then, applying a unique continuation property it follows that the origin is asymptotically stable for the damped models. Our proofs rely on the approach developed in Rosier (J Math Study 49:195–204, 2016) to study similar problems for the scalar BBM equation.
