Exponential asymptotic stability of repairable system with randomly selected repairman

2009 ◽  
Author(s):  
Xing Qiao ◽  
Dan Ma ◽  
Zhaoxing Li
Keyword(s):  
Asymptotic Stability ◽  
Repairable System ◽  
Exponential Asymptotic Stability

Exponential Asymptotic Stability of a Repairable System with Two Identical Components

2012 ◽  
Vol 591-593 ◽  
pp. 2428-2431
Author(s):  
Xue Feng ◽  
Ping Zuo ◽  
Hong Tu Hua ◽  
Xiao Yan Qi
Keyword(s):  
Asymptotic Stability ◽  
Compact Operator ◽  
Continuous Semigroup ◽  
Repairable System ◽  
Strongly Continuous Semigroup ◽  
Semi Group ◽  
Positive Contraction ◽  
Spectral Bound ◽  
Exponential Asymptotic Stability ◽  
Stability Of The Solution

The repairable system solution’s exponential asymptotic stability was discussed in this paper, First we prove that the positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equations describing a system with two identical components is a quasi-compact operator. Following the result that 0 is an eigenvalue of the operator with algebraic index one and the strongly continuous semi-group is contraction, we deduce that the spectral bound of the operator is zero. By the above results we obtain easily the exponential asymptotic stability of the solution of the repairable system.

Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues

2009 ◽  
Vol 20 (5) ◽  
pp. 431-459 ◽  
Author(s):  
M. AMAR ◽  
D. ANDREUCCI ◽  
P. BISEGNA ◽  
R. GIANNI
Keyword(s):  
Asymptotic Stability ◽  
Elliptic Equation ◽  
Electrical Conduction ◽  
Biological Tissues ◽  
Impedance Tomography ◽  
Uniform Estimates ◽  
Additional Information ◽  
Exponential Asymptotic Stability ◽  
Complex Coefficients ◽  
With Memory

We study an electrical conduction problem in biological tissues in the radiofrequency range, which is governed by an elliptic equation with memory. We prove the time exponential asymptotic stability of the solution. We provide in this way both a theoretical justification to the complex elliptic problem currently used in electrical impedance tomography and additional information on the structure of the complex coefficients appearing in the elliptic equation. Our approach relies on the fact that the elliptic equation with memory is the homogenisation limit of a sequence of problems for which we prove suitable uniform estimates.

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