scholarly journals Exponential decay and global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 795-826
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras ◽  
Djamel Ouchenane
Keyword(s):  
Exponential Decay ◽  
Source Term ◽  
Existence Of Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Distributed Delay ◽  
Viscoelastic System ◽  
Nonlinear Source ◽  
One Dimensional ◽  
Global Existence Of Solutions

We investigate in this work a singular one-dimensional viscoelastic system with a nonlinear source term, distributed delay, nonlocal boundary condition, and damping terms. By the theory of potentialwell, the existence of a global solution is established, and by the energy method and the functional of Lyapunov, we prove the exponential decay result. This work is an extension of Boulaaras? work in ([3] and [27]).

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 Global Existence and Decay for a System of Two Singular Nonlinear Viscoelastic Equations with General Source and Localized Frictional Damping Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nadia Mezouar ◽  
Ahmad Mohammed Alghamdi
Keyword(s):  
Boundary Condition ◽  
Lyapunov Functional ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Dimensional System ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
Frictional Damping ◽  
Viscoelastic Equations ◽  
General Source

The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

ON THE ZERO THICKNESS LIMIT OF THIN FERROMAGNETIC FILMS WITH SURFACE ANISOTROPY ENERGY

2001 ◽  
Vol 11 (08) ◽  
pp. 1469-1490 ◽  
Author(s):  
K. HAMDACHE ◽  
M. TILIOUA
Keyword(s):  
Maxwell Equations ◽  
Existence Of Solutions ◽  
Anisotropy Energy ◽  
Surface Anisotropy ◽  
Magnetic Polarization ◽  
One Dimensional ◽  
Ferromagnetic Films ◽  
Lifshitz Equation ◽  
Global Existence Of Solutions ◽  
Model Equations

We discuss the behaviour, when the thickness ε tends to 0, of thin ferromagnetic films with surface anisotropy energy. The model equations are given by the Landau–Lifshitz equation coupled to Maxwell equations with magnetic polarization. We consider two types of materials: flat and slender cylinders. Two scalings for the surface anisotropy coefficient are used. In the first one it is assumed that the coefficient is of order ε while in the second one we suppose that it is of order 1. We prove global existence of solutions and show that the zero-thickness limit induces new effects. For example, for slender media we get a nonlocal effect for the magnetic excitation while for flat media we obtain a one-dimensional magnetic field.

Thermal blow-up in a finite strip with superdiffusive properties

2018 ◽  
Vol 21 (4) ◽  
pp. 949-959
Author(s):  
Colleen M. Kirk ◽  
W. Edward Olmstead
Keyword(s):  
Energy Source ◽  
Diffusion Equation ◽  
Source Term ◽  
Blow Up ◽  
High Energy ◽  
Fractional Diffusion ◽  
The Other ◽  
Nonlinear Source ◽  
One Dimensional ◽  
Finite Strip

Abstract We investigate the problem of a high-energy source localized within a one-dimensional superdiffusive medium of finite length. The problem is modeled by a fractional diffusion equation with a nonlinear source term. For the boundary conditions, we consider both the case of homogeneous Dirichlet conditions and the case of homogeneous Neumann conditions. We investigate this model to determine whether or not blow-up occurs. It is demonstrated that a blow-up may or may not occur for the Dirichlet case. On the other hand, a blow-up is unavoidable for the Neumann case.

scholarly journals Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yingjie Zhu ◽  
Fuzhong Cong
Keyword(s):  
Global Existence ◽  
Cell Density ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Energy Estimates ◽  
Fast Diffusion ◽  
Chemotaxis Model ◽  
Nonlinear Source ◽  
Strongly Coupled ◽  
Global Existence Of Solutions

This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.

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