Preprint A304/2004
On the controllability and stabilization of
the linearized Benjamin-Ono equation

Jaime H. Ortega | Linares, Felipe

**Keywords: **
exact controllability | stabilization | Benjamin-Ono
equation | dispersive equation

In this work we are interested in the study of controllability and
stabilization of the linearized Benjamin-Ono equation with
periodic boundary conditions, which is a generic model for the
study of weakly nonlinear waves with nonlocal dispersion. It is
well known that the Benjamin-Ono equation has infinite number of
conserved quantities, thus we consider only controls acting in the
equation such that the volume of the solution is conserved. We
study also the stabilization with a feedback law which gives us an
exponential decay of the solutions.