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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 201682, 33 pages
Research Article

A Semigroup Approach to the System with Primary and Secondary Failures

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Received 2 July 2009; Accepted 22 February 2010

Academic Editor: Irena Lasiecka

Copyright © 2010 Abdukerim Haji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.