New general decay result for a class of neutral viscoelastic equations

2022 ◽  
Vol 506 (2) ◽  
pp. 125673
Author(s):  
Kun-Peng Jin ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
General Decay ◽  
Viscoelastic Equations

scholarly journals New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Adel M. Al-Mahdi ◽  
Salim A. Messaoudi
Keyword(s):  
Wide Class ◽  
Relaxation Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
General Assumption ◽  
General Decay ◽  
Source Terms ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
General Source

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .

scholarly journals General Decay and Blow-Up of Solutions for a System of Viscoelastic Equations of Kirchhoff Type with Strong Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Wenjun Liu ◽  
Gang Li ◽  
Linghui Hong
Keyword(s):  
Blow Up ◽  
Global Solutions ◽  
Initial Energy ◽  
General Decay ◽  
Strong Damping ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
Arbitrarily Positive Initial Energy

The general decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping is considered. We first establish two blow-up results: one is for certain solutions with nonpositive initial energy as well as positive initial energy by exploiting the convexity technique, the other is for certain solutions with arbitrarily positive initial energy based on the method of Li and Tsai. Then, we give a decay result of global solutions by the perturbed energy method under a weaker assumption on the relaxation functions.

scholarly journals Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fatma Ekinci ◽  
Erhan Pișkin ◽  
Salah Mahmoud Boulaaras ◽  
Ibrahim Mekawy
Keyword(s):  
Boundary Condition ◽  
Global Existence ◽  
Recent Work ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
General Decay ◽  
Quasilinear System ◽  
Relaxation Functions ◽  
Decay Of Solutions ◽  
Viscoelastic Equations

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.

New general decay of solutions in a porous-thermoelastic system with infinite memory

2021 ◽  
Vol 500 (1) ◽  
pp. 125136
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
General Decay ◽  
Infinite Memory ◽  
Decay Of Solutions
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