Dispersive equations: Controllability and stabilization in periodic domains

• Grant number: 20/14226-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2020
• End date: May 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Francisco Javier Vielma Leal
• Host 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].

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VIELMA LEAL, FRANCISCO J.; PASTOR, ADEMIR. TWO SIMPLE CRITERION TO OBTAIN EXACT CONTROLLABILITY AND STABILIZATION OF A LINEAR FAMILY OF DISPERSIVE PDE'S ON A PERIODIC DOMAIN. EVOLUTION EQUATIONS AND CONTROL THEORY, DEC 2021. (19/02512-5, 20/14226-4)

VIELMA LEAL, FRANCISCO J.; PASTOR, ADEMIR. CONTROL AND STABILIZATION FOR THE DISPERSION GENERALIZED BENJAMIN EQUATION ON THE CIRCLE. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, v. 28, p. 42-pg., 2022-08-02. (20/14226-4, 19/02512-5)

CAPISTRANO-FILHO, ROBERTO DE A.; KWAK, CHULKWANG; LEAL, FRANCISCO J. VIELMA. On the control issues for higher-order nonlinear dispersive equations on the circle. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 68, p. 42-pg., 2022-07-14. (20/14226-4)