TWO SIMPLE CRITERION TO OBTAIN EXACT CONTROLLABILITY AND STABILIZATION OF A LINEAR FAMILY OF DISPERSIVE PDE'S ON A PERIODIC DOMAIN

Author(s)

Vielma Leal, Francisco J. ^[1] ; Pastor, Ademir ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: EVOLUTION EQUATIONS AND CONTROL THEORY; DEC 2021.
• Web of Science Citations: 0

Abstract

In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in H-p(s)(T) with s is an element of R. We apply these results to prove that the linearized Smith equation, the linearized dispersion-generalized Benjamin-Ono equation, the linearized fourth-order Schrodinger equation, and the Higher-order Schrodinger equations are exactly controllable and exponentially stabilizable with any given decay rate in H-p(s)(T) with s is an element of R. (AU)

• FAPESP's process: 19/02512-5 - Systems and partial differential equations
• Grantee: Marcelo da Silva Montenegro
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 20/14226-4 - Dispersive equations: Controllability and stabilization in periodic domains
• Grantee: Francisco Javier Vielma Leal
• Support Opportunities: Scholarships in Brazil - Post-Doctoral