A Semigroup Approach to the System with Primary and Secondary Failures
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/201682 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |