A Semigroup Approach to the System with Primary and Secondary Failures

Abdukerim Haji

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-33

Abstract:

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 of -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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:201682

DOI: 10.1155/2010/201682

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