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 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 Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quang-Minh Tran ◽  
Hong-Danh Pham
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Decay Rate ◽  
Wave Equations ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Damping Term ◽  
General Decay Rate

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

scholarly journals A Novel Decay Rate for a Coupled System of Nonlinear Viscoelastic Wave Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 203 ◽  
Author(s):  
Khaled Zennir ◽  
Sultan S. Alodhaibi
Keyword(s):  
Decay Rate ◽  
Wave Equations ◽  
Local Existence ◽  
Coupled System ◽  
Initial Energy ◽  
Energy Estimates ◽  
Contraction Mapping Theorem ◽  
Strong Damping ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave

The main goal of the present paper is to study the existence, uniqueness and behavior of a solution for a coupled system of nonlinear viscoelastic wave equations with the presence of weak and strong damping terms. Owing to the Faedo-Galerkin method combined with the contraction mapping theorem, we established a local existence in [ 0 , T ] . The local solution was made global in time by using appropriate a priori energy estimates. The key to obtaining a novel decay rate is the convexity of the function χ , under the special condition of the initial energy E ( 0 ) . The condition of the weights of weak and strong damping has a fundamental role in the proof. The existence of both three different damping mechanisms and strong nonlinear sources make the paper very interesting from a mathematics point of view, especially when it comes to unbounded spaces such as R n .

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 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 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.

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