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Dispersive equations: Controllability and stabilization in periodic domains

Grant number: 20/14226-4
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): December 01, 2020
Effective date (End): November 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Ademir Pastor Ferreira
Grantee:Francisco Javier Vielma Leal
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:19/02512-5 - Systems and partial differential equations, AP.TEM

Abstract

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 [3].

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