SEMIGROUP METHODS FOR A PARALLEL MAINTENANCE SYSTEM WITH TWO COMPONENTS

2010 ◽  
Vol 08 (04) ◽  
pp. 363-386 ◽  
Author(s):  
ABDUKERIM HAJI ◽  
BILIKIZ YUNUS
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Theory ◽  
Positive Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Maintenance System ◽  
Time Dependent Solution

By using the theory of C0-semigroups and spectral theory of positive operators, we prove well-posedness of the parallel maintenance system with two components and study the asymptotic behavior of the time-dependent solution.

The well-Posedness of a Two-Unit Standby Redundant Electronic Equipment System

2013 ◽  
Vol 325-326 ◽  
pp. 315-318
Author(s):  
Xing Qiao ◽  
Yan Wang ◽  
Dan Ma ◽  
Zhuang Liu
Keyword(s):  
Steady State ◽  
Electronic Equipment ◽  
Time Dependent ◽  
Well Posedness ◽  
Reliability Study ◽  
Reliability Indices ◽  
Unique Existence ◽  
Human Failure ◽  
Time Dependent Solution ◽  
Equipment System

In this paper, we deal with a two-unit standby redundant electronic equipment system under human failure. In reliability study, it is ordinary to substitute the steady-state reliability indices for dynamic ones because the time-dependent solution is difficult to get. But this replacement should be based on some conditions in general. Therefore it is important to study the unique existence and the expression of the dynamic solution and it is the same with its stability.

Asymptotic behavior of small solutions of the Benjamin–Ono equation with time-dependent coefficients

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Youcef Mammeri
Keyword(s):  
Asymptotic Behavior ◽  
Time Scale ◽  
Time Dependent ◽  
Continuous Case ◽  
Well Posedness ◽  
Natural Time

AbstractWe study the behavior of small solutions depending on time of the generalized and regularized Benjamin–Ono equation in both continuous and periodic context. In particular, we prove that these solutions remain small for a time scale improving the natural time given by the local well-posedness. In the continuous case, the result becomes global-in-time.

scholarly journals A Semigroup Approach to the System with Primary and Secondary Failures

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
Abdukerim Haji
Keyword(s):  
Functional Analysis ◽  
Steady State ◽  
Asymptotic Stability ◽  
Positive Solution ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Semigroup Approach ◽  
Time Dependent Solution

We investigate the solution of a repairable parallel system with primary as well as secondary failures. By using the method of functional analysis, especially, the spectral theory of linear operators and the theory ofC0-semigroups, we prove well-posedness of the system and the existence of positive solution of the system. And then we show that the time-dependent solution strongly converges to steady-state solution, thus we obtain the asymptotic stability of the time-dependent solution.

scholarly journals On Asymptotic Behavior of the Time-Dependent Solution of a Reliability Model

2014 ◽  
Vol 2 ◽  
pp. 1-11 ◽  
Author(s):  
Geni Gupur
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Steady State Solution ◽  
State Solution ◽  
Time Dependent ◽  
Reliability Model ◽  
Repair Rate ◽  
Lipschitz Continuous ◽  
Time Dependent Solution

On the basis of our previous work we study asymptotic behavior of the time-dependent solution of a reliability model of two identical units and a repairman and prove the following result: If the repair rate μ(x) is Lipschitz continuous and there exist two positive constants μ and μ such that 0 < μ ≤μ(x)≤ μ < ∞, then its time-dependent solution exponentially converges to its steady-state solution.

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