scholarly journals Growth of solutions with $ L^{2(p+2)} $-norm for a coupled nonlinear viscoelastic Kirchhoff equation with degenerate damping terms

2021 ◽  
Vol 7 (1) ◽  
pp. 371-383
Author(s):  
Abdelbaki Choucha ◽  
◽  
Muajebah Hidan ◽  
Bahri Cherif ◽  
Sahar Ahmed Idris ◽  
...  
Keyword(s):  
Initial Data ◽  
Point Of View ◽  
Kirchhoff Equation ◽  
Source Terms ◽  
Kirchhoff Equations ◽  
Energy Point ◽  
Nonlinear Viscoelastic ◽  
Growth Of Solutions

<abstract><p>In this work, we consider a coupled nonlinear viscoelastic Kirchhoff equations with degenerate damping, dispersion and source terms. Under suitable hypothesis, we will prove that when the initial data are large enough (in the energy point of view), the energy grows exponentially and thus so the $ L^{2(p+2)} $-norm.</p></abstract>

scholarly journals Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Erhan Pişkin
Keyword(s):  
Initial Data ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Initial Boundary ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Positive Initial Energy ◽  
Damping And Source Terms ◽  
Growth Of Solutions

We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

Evaluation Of The Functional Of Space-Planning Arrangement Of A Building

2019 ◽  
pp. 4-9
Keyword(s):  
Numerical Simulation ◽  
Life Cycle ◽  
Initial Data ◽  
Objective Assessment ◽  
Objective Evaluation ◽  
Point Of View ◽  
Shopping Centers ◽  
Space Planning ◽  
Planning Decisions ◽  
The Cost

The article focuses on the problem of the lack of objective evaluation of space-planning arrangement of buildings as a creative approach of the architect to the performing of functional tasks by the object. It is proposed to create a methodology for assessing the functional of space-planning solutions of buildings on the basis of numerical simulation of functional processes using the theory of human flows. There is a description of the prospects of using this method, which makes it possible to increase the coefficient of compactness, materials and works saving, more efficient use of space, reduce the cost of the life cycle of the building, save human forces and time to implement the functional of the building. The necessary initial data for modeling on the example of shopping and shopping-entertainment centers are considered. There are three main tasks for algorithmization of the functional of shopping centers. The conclusion is made about necessity of development of a method for objective assessment of buildings from the point of view of ergonomics of space-planning decisions based on the study of human behavior in buildings of different purposes.

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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