Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type

José R. Quintero; Alex M. Montes

doi:10.3934/eect.2021021

Article Contents

2022, Volume 11, Issue 3: 681-709. Doi: 10.3934/eect.2021021

This issue Previous Article Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations Next Article On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping

Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type

José R. Quintero^1, and
Alex M. Montes^2, ,

1.
Mathematics Department, Universidad del Valle, Cali, Valle del Cauca, Colombia
2.
Mathematics Department, Universidad del Cauca, Popayán, Cauca, Colombia

^* Corresponding author: Alex M. Montes
^* Corresponding author: Alex M. Montes

Received: June 30, 2020

Revised: January 31, 2021

Published: June 2022

JRQ is supported by the Mathematics Department at Universidad del Valle and AMM is supported by the Mathematics Department at Universidad del Cauca

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Abstract

In this work we consider the exact controllability and stabilization on a periodic domain for the generalized Benjamin-Ono type system for internal waves. The exact controllability of the linearized model is proved by using the moment method and spectral analysis. In order to get the same result for the nonlinear model, we use a fixed point argument in Sobolev spaces.

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Mathematics Subject Classification: Primary: 93B05, 93D15; Secondary: 35Q35.

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References

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