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A Semigroup Approach to the System with Primary and Secondary Failures

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Author(s): Abdukerim Haji

Journal: International Journal of Mathematics and Mathematical Sciences
ISSN 0161-1712

Volume: 2010;
Date: 2010;
Original page

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 C0-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.
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