General decay for a quasilinear system of viscoelastic equations with nonlinear damping

2012 ◽  
Vol 32 (4) ◽  
pp. 1321-1332
Author(s):  
Jong Yeoul Park ◽  
Sun Hye Park
Keyword(s):  
Nonlinear Damping ◽  
General Decay ◽  
Quasilinear System ◽  
Viscoelastic Equations

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.

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 rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

General decay of a nonlinear damping porous-elastic system with past history

2019 ◽  
Vol 65 (2) ◽  
pp. 249-275
Author(s):  
Houssem Eddine Khochemane ◽  
Lamine Bouzettouta ◽  
Salah Zitouni
Keyword(s):  
Elastic System ◽  
Past History ◽  
Nonlinear Damping ◽  
General Decay

Well-posedness and general decay of a nonlinear damping porous-elastic system with infinite memory

2020 ◽  
Vol 61 (2) ◽  
pp. 021505 ◽  
Author(s):  
Houssem Eddine Khochemane ◽  
Abdelhak Djebabla ◽  
Salah Zitouni ◽  
Lamine Bouzettouta
Keyword(s):  
Elastic System ◽  
Nonlinear Damping ◽  
General Decay ◽  
Well Posedness ◽  
Infinite Memory
Sign in / Sign up

Export Citation Format

Share Document