scholarly journals On a Couple of Nonlocal Singular Viscoelastic Equations with Damping and General Source Terms: Blow-Up of Solutions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Erhan Piskin ◽  
Salah Mahmoud Boulaaras ◽  
Hasan Kandemir ◽  
Bahri Belkacem Cherif ◽  
Mohamed Biomy
Keyword(s):  
Blow Up ◽  
Source Terms ◽  
Viscoelastic Equations ◽  
Damping And Source Terms ◽  
General Source

Under some given conditions, we prove the explosion result of the solution of the system of nonlocal singular viscoelastic with damping and source terms on general case. This current study is a general case of the previous work of Boulaaras.

scholarly journals Blow up of solutions for a system of two singular nonlocal viscoelastic equations with damping, general source terms and a wide class of relaxation functions

2021 ◽  
Vol 6 (5) ◽  
pp. 4664-4676 ◽  
Author(s):  
Salah Boulaaras ◽  
◽  
Abdelbaki Choucha ◽  
Bahri Cherif ◽  
Asma Alharbi ◽  
...  
Keyword(s):  
Wide Class ◽  
Blow Up ◽  
Source Terms ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
General Source

Blow Up of Solutions for a Viscoelastic System with Damping and Source Terms in IRn

2010 ◽  
Vol 65 (5) ◽  
pp. 392-400 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Coupled System ◽  
Initial Energy ◽  
Source Terms ◽  
Viscoelastic System ◽  
Positive Initial Energy ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

This paper deals with a Cauchy problem for the coupled system of nonlinear viscoelastic equations with damping and source terms. We prove a new finite time blow-up result for compactly supported initial data with non-positive initial energy as well as positive initial energy by using the modified energy method and the compact support technique.

scholarly journals Blow-Up of Solutions for a Coupled Nonlinear Viscoelastic Equation with Degenerate Damping Terms: Without Kirchhoff Term

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Salah Mahmoud Boulaaras ◽  
Abdelbaki Choucha ◽  
Mohamed Abdalla ◽  
Karthikeyan Rajagopal ◽  
Sahar Ahmed Idris
Keyword(s):  
Blow Up ◽  
Quasilinear System ◽  
Source Terms ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and source terms without the Kirchhoff term. Under suitable hypothesis, we study the blow-up of solutions.

scholarly journals Blow-up of solutions for a quasilinear system with degenerate damping terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Salah Boulaaras ◽  
Abdelbaki Choucha ◽  
Praveen Agarwal ◽  
Mohamed Abdalla ◽  
Sahar Ahmed Idris
Keyword(s):  
Blow Up ◽  
Quasilinear System ◽  
Source Terms ◽  
Viscoelastic Equations ◽  
General Source

AbstractIn this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the general case of the recent results of Boulaaras’ works (Bull. Malays. Math. Sci. Soc. 43:725–755, 2020) and (Appl. Anal. 99:1724–1748, 2020).

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 ) .

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