College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Copyright © 2010 Abdukerim Haji. This is an open access article distributed under the
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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