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

Abstract

We investigate the exact control problem associated to the linearized dispersion-generalized Benjamin–Ono equation which contains fractional-order spatial derivatives on a periodic domain, \(\mathbb {T}\). More specifically, we establish that a mass-preserving external force can be applied to the linear system to achieve a final state from a given initial state. The stabilization problem with a linear feedback control is also studied.

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Acknowledgements

The author thanks Derek Smith and Seungly Oh for fruitful conversations and Felipe Linares for helpful comments as well as the referee’s remarks which improve the presentation of this work.

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Correspondence to C. Flores.

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Flores, C. Control and stability of the linearized dispersion-generalized Benjamin–Ono equation on a periodic domain. Math. Control Signals Syst. 30, 13 (2018). https://doi.org/10.1007/s00498-018-0219-z

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Keywords

  • Controllability
  • Stabilization
  • Linear KdV-like equations
  • Dispersive equations

Mathematics Subject Classification

  • 35Q93
  • 93D15
  • 93B52