Affiliations: Shanghai Key Laboratory for Contemporary Applied Mathematic, Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail: dqli@fudan.edu.cn | Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France. E-mail: bopeng.rao@math.unistra.fr
Note: [] Corresponding author: Tatsien Li, Shanghai Key Laboratory for Contemporary Applied Mathematic, Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail: dqli@fudan.edu.cn
Abstract: In this paper, the asymptotic null controllability and various kinds of asymptotic synchronization, as some sorts of weakened controllability and synchronization, are introduced and studied for a coupled system of wave equations with Dirichlet boundary controls. Equivalent properties of observability are established and several examples of explanation are also given.
Keywords: asymptotic null controllability, D-observability, asymptotic synchronization, asymptotic null controllability and synchronization by groups, asymptotic synchronization by groups, CD-observability
