A note on the exact synchronization by groups for a coupled system of wave equations

2014 ◽  
Vol 38 (13) ◽  
pp. 2803-2808 ◽  
Author(s):  
Tatsien Li ◽  
Bopeng Rao
Keyword(s):  
Wave Equations ◽  
Coupled System

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

scholarly journals Generalized approximate boundary synchronization for a coupled system of wave equations

2020 ◽  
Author(s):  
Yanyan Wang
Keyword(s):  
Wave Equations ◽  
Dirichlet Boundary ◽  
Coupled System ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Exact Boundary ◽  
Boundary Controls ◽  
The Relationship ◽  
Exact Boundary Synchronization ◽  
Dirichlet Boundary Controls

In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyse the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman’s matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state, and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.

Stability for a nonlinear coupled system of elasticity and thermoelasticity with second sound

2014 ◽  
Vol 13 (01) ◽  
pp. 45-75 ◽  
Author(s):  
Yi-Ping Meng ◽  
Ya-Guang Wang
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Middle Part ◽  
Second Sound ◽  
Qualitative Properties ◽  
Thermal Change ◽  
Nonlinear Coupled System ◽  
Initial Boundary Value

In this paper, we study the qualitative properties of solutions to a nonlinear system describing the motion of a bar in which the middle part is sensitive to the thermal change, while the outer parts are insensible. By the energy method, we show that the initial boundary value problem for this coupled system of wave equations and thermoelastic equations with second sound in one space variable is well-posed globally in time, and it is also stable exponentially as the time goes to infinity when the wave speed of the outer parts is properly large, under certain restrictions on the initial data and the growth rate of the nonlinear terms.

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