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Control and stability of the linearized dispersion-generalized Benjamin-Ono equation on a periodic domain. (English) Zbl 1401.93036

Summary: 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.

MSC:

93B05 Controllability
93B17 Transformations
93D15 Stabilization of systems by feedback
35Q53 KdV equations (Korteweg-de Vries equations)
93C20 Control/observation systems governed by partial differential equations
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