Exact boundary synchronization for a kind of first order hyperbolic system

¹ School of Mathematical Sciences, Fudan University, Shanghai Key Laboratory for Contemporary Applied Mathematic; Nonlinear Mathematical Modeling and Methods Laboratory, 200433 Shanghai, China
² School of Mathematics, Southeast University, 211189 Nanjing, China

^* Project supported by the National Natural Science Foundation of China (No 11831011).
^*** Project supported by the National Natural Science Foundation of China (No 11901082), the Natural Science Foundation of Jiangsu Province (BK20190323), and the Fundamental Research Funds for the Central Universities.
^** Corresponding author: xinglu@seu.edu.cn

Received: 5 September 2021
Accepted: 18 April 2022

Abstract

In recent years there have been many in-depth researches on the boundary controllability and boundary synchronization for coupled systems of wave equations with various types of boundary conditions. In order to extend the study of synchronization from wave equations to a much larger range of hyperbolic systems, in this paper we will define and establish the exact boundary synchronization for the first order linear hyperbolic system based on previous work on its exact boundary controllability. The determination and estimate of exactly synchronizable states and some related problems are also discussed. This work can be applied to a great deal of diverse systems, and a new perspective to study the synchronization problem for the coupled system of wave equations can be also provided.