On the controllability of the improved Boussinesq equation *

Contrôlabilité de l'équation de Boussinesq améliorée

Eduardo Cerpa (1) , Emmanuelle Crépeau (2)

1 Departamento de Matematica, Universidad Tecnica Federico Santa Maria
2 LMV - Laboratoire de Mathématiques de Versailles

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls are considered. Under some condition on the velocity to which the control moves, exact controllability results for both linear and nonlinear improved Boussinesq equations are obtained applying the moment method and a fixed point argument.

Mots clés: Boussinesq type equation; exact controllability; approximate controllability; spectral analysis; moving control; moment method

Domaines: Optimisation et contrôle [math.OC]

Eduardo Cerpa, Emmanuelle Crépeau. On the controllability of the improved Boussinesq equation *. 2017. ⟨hal-01661174⟩