Stabilization of Kawahara equation with saturated internal or boundary feedback controls
Résumé
In this paper, we study the stabilizability of the Kawahara equation in a bounded interval (0,L) by a saturated internal control and boundary feedback. We prove the exponential stabilization of the corresponding closed-loop system. We first show the well-posedness of the nonlinear system using linear, nonlinear semigroup theory and fixed-point arguments. Next, we prove two stabilization results by means of interior-saturating feedback and boundary-saturated feedback as well, using observability inequalities and certain unique continuation principle.
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