scholarly journals On the stability of a laminated Timoshenko problem with interfacial slip in the whole space under frictional dampings or infinite memories

2020 ◽  
Vol 7 (1) ◽  
pp. 194-218
Author(s):  
Aissa Guesmia
Keyword(s):  
Initial Data ◽  
Hyperbolic Equations ◽  
Weight Functions ◽  
Stability Estimates ◽  
Interfacial Slip ◽  
Infinite Memory ◽  
Bounded Interval ◽  
Frictional Damping ◽  
Stability And Instability ◽  
The Stability

Abstract The author of the present paper considered in [16] a model describing a vibrating strucure of an interfacial slip and consists of three coupled hyperbolic equations in one-dimensional bounded interval, where the dissipation is generated by either a frictional damping or an infinite memory, and it is acting only on one component. Some strong, polynomial, exponential and non exponential stability results were proved in [16] depending on the values of the parameters and the regularity of the initial data. The objective of the present paper is to compelete the study of [16] by considering this model in the whole line ℝ and under only one control given by a frictional damping or an infinite memory. When the system is controled via its second or third component (rotation angle displacement or dynamic of the slip), we show that this control alone is sufficient to stabilize our system and get different polynomial stability estimates in the L 2-norm of the solution and its higher order derivatives with respect to the space variable. The decay rate depends on the regularity of the initial data, the nature of the control and the parameters in the system. However, when the system is controled via its first component (transversal displacement), we found a new stability condition depending on the parameters in the system. This condition defines a limit between the stability and instability of the system in the sense that, when this condition is staisfied, the system is polynomially stable. Otherwise, when this condition is not satisfied, we prove that the solution does not converge to zero at all. The proofs are based on the energy method and Fourier analysis combined with judicious choices of weight functions.

scholarly journals Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations

2005 ◽  
Vol 2005 (2) ◽  
pp. 183-213 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Pavel E. Sobolevskii
Keyword(s):  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
High Order ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
Accuracy Difference ◽  
High Order Of Accuracy ◽  
The Stability

We consider the abstract Cauchy problem for differential equation of the hyperbolic typev″(t)+Av(t)=f(t)(0≤t≤T),v(0)=v0,v′(0)=v′0in an arbitrary Hilbert spaceHwith the selfadjoint positive definite operatorA. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on the three points for the numerical solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are established. In applications, the stability estimates for the solutions of the high order of accuracy difference schemes of the mixed-type boundary value problems for hyperbolic equations are obtained.

Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors

1997 ◽  
Vol 127 (4) ◽  
pp. 781-796 ◽  
Author(s):  
Harumi Hattori
Keyword(s):  
Steady State ◽  
Initial Data ◽  
Positive Constant ◽  
Hydrodynamic Model ◽  
Steady State Solution ◽  
Doping Profile ◽  
Asymptotically Stable ◽  
Stability And Instability ◽  
The Stability ◽  
Steady State Solutions

We discuss the stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the special variable x. We shall show that a given steady-state solution is asymptotically stable or unstable, depending on whether or not the density of the initial data satisfies P = 0, where P is defined in (3.12).

scholarly journals A note on the difference schemes for hyperbolic equations

2001 ◽  
Vol 6 (2) ◽  
pp. 63-70 ◽  
Author(s):  
A. Ashyralyev ◽  
P. E. Sobolevskii
Keyword(s):  
Hilbert Space ◽  
Initial Value Problem ◽  
Hyperbolic Equations ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Initial Value ◽  
Order Accuracy ◽  
Accuracy Difference ◽  
The Difference ◽  
The Stability

The initial value problem for hyperbolic equationsd 2u(t)/dt 2+A u(t)=f(t)(0≤t≤1),u(0)=φ,u′(0)=ψ, in a Hilbert spaceHis considered. The first and second order accuracy difference schemes generated by the integer power ofAapproximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

The identity policy and its effect in the stability of Middle East after 2010

2019 ◽  
pp. 434
Author(s):  
Ali Hussein Kadhim Alesammi
Keyword(s):  
Middle East ◽  
International Relations ◽  
Social Construct ◽  
Stability And Instability ◽  
The Social ◽  
The Stability ◽  
International Interactions ◽  
Regional Interests ◽  
Political Groups ◽  
Identity Policy

Since 2010 Middle East have many events or what they call "Arab spring events" which it result of overthrow governments and the rise of new political groups, all of this elements was resulting of many international and regional activities and making new regional and international axles, as well as the intersections of the different regional interests, therefore this research will try to study the stability and instability in the region as an independent variable not according to the neorealism or neoliberalism theories, but according to the constructivism theory which it base their assumptions on:  "In the international relations the non-physical structures of international interactions are determined by the identities of the players, which in turn determine the interests that determine the behavior of international players." So the research questions are: 1-What is the identity policy and haw affect in international relations? 2-How the social construct affect in international relations? 3-How the elite's identities for the main actors in the Middle East affect in the regional axles?  

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

scholarly journals Stability and Instability in the Lysogenic State of Phage Lambda

2010 ◽  
Vol 192 (22) ◽  
pp. 6064-6076 ◽  
Author(s):  
John W. Little ◽  
Christine B. Michalowski
Keyword(s):  
Intrinsic Rate ◽  
Growth Conditions ◽  
Emergent Properties ◽  
Regulatory Circuits ◽  
Stability And Instability ◽  
Natural Range ◽  
Analysis Of Stability ◽  
Stable Association ◽  
The Stability ◽  
Gene Regulatory Circuits

ABSTRACT Complex gene regulatory circuits exhibit emergent properties that are difficult to predict from the behavior of the components. One such property is the stability of regulatory states. Here we analyze the stability of the lysogenic state of phage λ. In this state, the virus maintains a stable association with the host, and the lytic functions of the virus are repressed by the viral CI repressor. This state readily switches to the lytic pathway when the host SOS system is induced. A low level of SOS-dependent switching occurs without an overt stimulus. We found that the intrinsic rate of switching to the lytic pathway, measured in a host lacking the SOS response, was almost undetectably low, probably less than 10−8/generation. We surmise that this low rate has not been selected directly during evolution but results from optimizing the rate of switching in a wild-type host over the natural range of SOS-inducing conditions. We also analyzed a mutant, λprm240, in which the promoter controlling CI expression was weakened, rendering lysogens unstable. Strikingly, the intrinsic stability of λprm240 lysogens depended markedly on the growth conditions; lysogens grown in minimal medium were nearly stable but switched at high rates when grown in rich medium. These effects on stability likely reflect corresponding effects on the strength of the prm240 promoter, measured in an uncoupled assay system. Several derivatives of λprm240 with altered stabilities were characterized. This mutant and its derivatives afford a model system for further analysis of stability.

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