scholarly journals On Global Solvability and Asymptotic Behavior of a Nonlinear Coupled System with Memory Condition at the Boundary

2004 ◽  
Vol 11 (2) ◽  
pp. 297-313
Author(s):  
M. L. Santos ◽  
J. Ferreira ◽  
C. A. Raposo
Keyword(s):  
Asymptotic Behavior ◽  
Coupled System ◽  
Global Solvability ◽  
Memory Condition ◽  
Nonlinear Coupled System ◽  
With Memory

scholarly journals Decay rates for solutions of a Timoshenko system with a memory condition at the boundary

2002 ◽  
Vol 7 (10) ◽  
pp. 531-546 ◽  
Author(s):  
Mauro de Lima Santos
Keyword(s):  
Asymptotic Behavior ◽  
Energy Decay ◽  
Decay Rates ◽  
Memory Condition ◽  
Timoshenko System ◽  
Relaxation Functions ◽  
Rate Of Decay ◽  
With Memory

We consider a Timoshenko system with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decays exponentially and polynomially when the relaxation functions decays polynomially.

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.

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