Asymptotic synchronization of a coupled system of wave equations on a rectangular domain with reflecting sides

Article type: Research Article

Authors: Li, Tatsien^{a; *} | Rao, Bopeng^{b; c}

Affiliations: [a] 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 | [b] Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France. E-mail: bopeng.rao@math.unistra.fr | [c] School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Correspondence: [*] Corresponding author. E-mail: dqli@fudan.edu.cn.

Abstract: We show the sufficiency of Kalman’s rank condition for the uniqueness of solution to a coupled system of wave equations in a rectangular domain. The approach does not need any gap condition on the spectrum of the differential operator and the usual multiplier geometrical condition. Then, the study on the asymptotic synchronization by groups can be improved for the corresponding system.

Keywords: Fourier analysis, uniqueness theorem, Kalman’s rank condition, asymptotic synchronization, coupled system of wave equations

DOI: 10.3233/ASY-211699

Journal: Asymptotic Analysis, vol. 128, no. 1, pp. 85-102, 2022