Global existence and energy decay of solutions for the wave equation with a time varying delay term in the weakly nonlinear internal feedbacks

2012 ◽  
Vol 53 (12) ◽  
pp. 123514 ◽  
Author(s):  
Abbes Benaissa ◽  
Abdelkader Benaissa ◽  
Salim. A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Energy Decay ◽  
Time Varying ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Time Varying Delay ◽  
Decay Of Solutions ◽  
Varying Delay

scholarly journals Global existence and energy decay of solutions for a wave equation with a time-varying delay term

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 32-46
Author(s):  
Benguessoum Aissa
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Time Varying ◽  
Rate Estimate ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Decay Of Solutions ◽  
Varying Delay

We consider, in a bounded domain, a certain wave equation with a weak internal time-varying delay term. Under appropriate conditions, we prove global existence of solutions by the Faedo-Galerkin method and establish a decay rate estimate for the energy using the multiplier method.

scholarly journals Global Existence and Decay of Solutions for Coupled Nondegenerate Kirchhoff System with a Time Varying Delay Term

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Nadia Mezouar ◽  
Salah Mahmoud Boulaaras ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Global Existence ◽  
Stability Estimate ◽  
Time Varying ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Nonlinear Viscoelastic ◽  
Decay Of Solutions ◽  
Weight Condition ◽  
Varying Delay

This paper deals with the global existence of solutions in a bounded domain for nonlinear viscoelastic Kirchhoff system with a time varying delay by using the energy and Faedo–Galerkin method with respect to the delay term weight condition in the feedback and the delay speed. Furthermore, by using some convex functions properties, we prove a uniform stability estimate.

scholarly journals Stabilization of the Wave Equation with Boundary Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hao Li ◽  
Changsong Lin ◽  
Shupeng Wang ◽  
Yanmei Zhang
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Nonlinear Boundary ◽  
Variable Coefficients ◽  
Time Varying ◽  
Closed Loop System ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Time Varying Delay ◽  
Varying Delay

We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.

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