2019
DOI: 10.1088/1361-6544/aafe34
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On the well-posedness and large-time behavior of higher order Boussinesq system

Abstract: A family of Boussinesq systems has been proposed to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investigate the well-posedness and boundary stabilization of the generalized higher order Boussinesq systems of Korteweg-de Vries-type posed on a interval. We design a two-parameter family of feedback laws for which the system is locally well-posed and the solutions of the linearized system are exponentially decreasing in time.Date: 2018-08… Show more

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Cited by 3 publications
(4 citation statements)
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“…However, in order to prove the well-posedness of the resulting nonlinear system more regularity of the solutions is needed. For instance, in [6,7] a Kato smoothing effect was derived when a different set of boundary conditions is considered and some additional assumptions on the parameters are imposed. In our case, the study of the controllability properties when b 1 = d 1 = 0 remains open.…”
Section: The Nonlinear Systemmentioning
confidence: 99%
See 3 more Smart Citations
“…However, in order to prove the well-posedness of the resulting nonlinear system more regularity of the solutions is needed. For instance, in [6,7] a Kato smoothing effect was derived when a different set of boundary conditions is considered and some additional assumptions on the parameters are imposed. In our case, the study of the controllability properties when b 1 = d 1 = 0 remains open.…”
Section: The Nonlinear Systemmentioning
confidence: 99%
“…where λ, μ ∈ R are modelling parameters that do not possess a direct physical interpretation as does θ (observe that (7) follows from ( 8)). Similar but more elaborate restrictions apply to the parameters in (1).…”
Section: Introductionmentioning
confidence: 99%
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