We intent to establish new results related to Section 5 of the thematic project. Our first aimis to study controllability and stabilization for a generalized Benjamin type equation. Recentresults regarding controllability and stabilization of the Benjamin equation on a periodic domainhave been obtained by Panthee and Vielma Leal (see [5, 6]). Furthermore, the authors provedthat the Benjamin equation is globally exactly controllable and globally exponentially stabilizable.Our goal is then to extend these results to a wide class of dispersive models. Beside the ideasin [5, 6] we intent to explore the strategies in [7, 4, 1, 2]. As a second aim, We are interestedin completing the study on the controllability and stabilization properties of the Camassa-Holmequation initiated by Glass .
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