Control and stability of the linearized dispersion-generalized Benjamin–Ono equation on a periodic domain

Flores, Cynthia

doi:10.1007/s00498-018-0219-z

Cited by 2 publications

(2 citation statements)

References 39 publications

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“…In this sense (6.10) defines a continuum of equations of dispersive strength intermediate to two celebrated models. Regarding control and stabilization properties, the author in [11] proved that the LDGBO equation with α ∈ (1, 2) is exactly controllable in H s p (T) with s ≥ 0 and exponentially stabilizable in L 2 p (T). Here we extend these results to the (periodic) Sobolev space H s p (T) with s ∈ R, for any α > 0.…”

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confidence: 99%

Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain

Leal

Pastor

2022

EECT

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<p style='text-indent:20px;'>In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in <inline-formula><tex-math id="M1">\begin{document}$ H_{p}^{s}(\mathbb{T}) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ s\in \mathbb{R}. $\end{document}</tex-math></inline-formula> We apply these results to prove that the linearized Smith equation, the linearized dispersion-generalized Benjamin-Ono equation, the linearized fourth-order Schrödinger equation, and the Higher-order Schrödinger equations are exactly controllable and exponentially stabilizable with any given decay rate in <inline-formula><tex-math id="M3">\begin{document}$ H_{p}^{s}(\mathbb{T}) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M4">\begin{document}$ s\in \mathbb{R}. $\end{document}</tex-math></inline-formula></p>

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confidence: 99%

Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain

Leal

Pastor

2022

EECT

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“…Recently, Flores et al [34,35], studied the controllability and stabilization properties for the dispersion-generalized Benjamin-Ono equation in T. As a future work, we believe it is possible to apply the techniques used in [34,35] to obtain the controllability and stabilization for a generalized Benjamin type equation on a periodic domain.…”

Section: Semi-global Exponential Stabilization In L 2 0 Ptqmentioning

confidence: 96%

Study of solutions to some non-linear evolution equations of dispersive type

Javier Vielma Leal

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Control and stability of the linearized dispersion-generalized Benjamin–Ono equation on a periodic domain

Cited by 2 publications

References 39 publications

Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain

Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain

Study of solutions to some non-linear evolution equations of dispersive type

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