Global existence and decay of solutions of a singular nonlocal viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized damping term

2020 ◽  
Vol 43 (10) ◽  
pp. 6140-6164 ◽  
Author(s):  
Salah Boulaaras ◽  
Nadia Mezouar
Keyword(s):  
Boundary Condition ◽  
Global Existence ◽  
Source Term ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Damping Term ◽  
Viscoelastic System ◽  
Nonlinear Source ◽  
Decay Of Solutions ◽  
Localized Damping

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]).

Global Existence and Blow-Up of Solutions for a Porous Medium Equation

2012 ◽  
Vol 461 ◽  
pp. 532-536
Author(s):  
Yun Zhu Gao ◽  
Xi Meng ◽  
Hong Gai
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Global Existence ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Porous Medium Equation ◽  
Local Source ◽  
Medium Equation ◽  
The Fixed Point Theorem

In this paper, a porous medium equation with local source and nonlocal boundary condition is studied. By using the fixed point theorem and comparison principle. The global existence and blow-up of solutions are obtained .

scholarly journals Blowup Properties for a Semilinear Reaction-Diffusion System with Nonlinear Nonlocal Boundary Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Dengming Liu ◽  
Chunlai Mu
Keyword(s):  
Boundary Condition ◽  
Global Existence ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Nonlocal Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Subsolution And Supersolution

We investigate the blowup properties of the positive solutions for a semilinear reaction-diffusion system with nonlinear nonlocal boundary condition. We obtain some sufficient conditions for global existence and blowup by utilizing the method of subsolution and supersolution.

scholarly journals An inverse source problem for a two terms time-fractional diffusion equation

2021 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Fatima Dib ◽  
Mokhtar Kirane
Keyword(s):  
Boundary Condition ◽  
Fractional Derivatives ◽  
Source Term ◽  
Space Variable ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Integral Type ◽  
Time Fractional Diffusion Equation

In this paper, we consider an inverse problem for a linear heat equation involving two time-fractional derivatives, subject to a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution with an over- determining function of integral type.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

scholarly journals Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hongliang Gao ◽  
Xiaoling Han
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary conditionD0+αu(t)+a(t)f(t,u(t))=0,0<t<1,u(0)=0,u(1)=∑i=1∞αiu(ξi)is considered, where1<α≤2is a real number,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),  αi∈[0,∞)with∑i=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).

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