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 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 of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Nadia Mezouar ◽  
Salah Mahmoud Boulaaras ◽  
Ali Allahem
Keyword(s):  
Existence Of Solutions ◽  
Local Existence ◽  
Stability Estimate ◽  
Kirchhoff Equation ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Nonlinear Viscoelastic ◽  
Global And Local

In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature.

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