scholarly journals Global existence and asymptotic behavior for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, distributed delay and Balakrishnan-Taylor damping terms

2021 ◽  
Vol 7 (3) ◽  
pp. 4517-4539
Author(s):  
Abdelbaki Choucha ◽  
◽  
Salah Boulaaras ◽  
Asma Alharbi ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

<abstract><p>A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, Balakrishnan-Taylor damping, dispersion and distributed delay terms is studied. We establish the global existence of the solutions of the problem and by the energy method we prove an explicit and general decay rate result under suitable hypothesis.</p></abstract>

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

scholarly journals Global Existence for Two Singular One-Dimensional Nonlinear Viscoelastic Equations with respect to Distributed Delay Term

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Ali Allahem
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Energy Method ◽  
Distributed Delay ◽  
Potential Well ◽  
One Dimensional ◽  
Delay Term ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equations ◽  
General Source

In this current work, we are interested in a system of two singular one-dimensional nonlinear equations with a viscoelastic, general source and distributed delay terms. The existence of a global solution is established by the theory of potential well, and by using the energy method with the function of Lyapunov, we prove the general decay result of our system.

scholarly journals GENERAL DECAY OF SOLUTION FOR COUPLED SYSTEM OF VISCOELASTIC WAVE EQUATIONS OF KIRCHHOFF TYPE WITH DENSITY IN Rn

2017 ◽  
pp. 1073
Author(s):  
Abbes Benaissa ◽  
Abderrahmane Beniani ◽  
Khaled Zennir
Keyword(s):  
Decay Rate ◽  
Density Function ◽  
Wave Equations ◽  
Coupled System ◽  
General Decay ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Relaxation Functions ◽  
Viscoelastic Wave

A system of viscoelastic wave equations of Kirchhoff type is considered. For a wider class of relaxation functions, we use spaces weighted by the density function to establish a very general decay rate of the solution.

scholarly journals Existence and decay of solution to coupled system of viscoelastic wave equations with strong damping in Rn

2021 ◽  
Vol 39 (6) ◽  
pp. 31-52
Author(s):  
Keltoum Bouhali ◽  
Fateh Ellaggoune
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Decay Rate ◽  
Density Function ◽  
Sobolev Spaces ◽  
Energy Method ◽  
Wave Equations ◽  
Coupled System ◽  
General Decay Rate ◽  
Viscoelastic Wave

In this paper, we establish a general decay rate properties of solutions for a coupled system of viscoelastic wave equations in IRn under some assumptions on g1; g2 and linear forcing terms. We exploit a density function to introduce weighted spaces for solutions and using an appropriate perturbed energy method. The questions of global existence in the nonlinear cases is also proved in Sobolev spaces using the well known Galerkin method.

scholarly journals On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Salem Alkhalaf ◽  
Ibrahim Mekawy ◽  
...  
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Energy Method ◽  
Existence Of Solutions ◽  
Distributed Delay ◽  
Stability Result ◽  
Kirchhoff Equations ◽  
Global Existence Of Solutions

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

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.

scholarly journals General Decay Rate of Solution for Love-Equation with Past History and Absorption

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1632
Author(s):  
Khaled Zennir ◽  
Mohamad Biomy
Keyword(s):  
Decay Rate ◽  
Source Term ◽  
Blow Up ◽  
Past History ◽  
Point Of View ◽  
General Decay ◽  
General Decay Rate ◽  
Infinite Memory ◽  
New Class ◽  
The Relationship

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

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