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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| 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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| _version_ | 1832556129151877120 |
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| author | Abdukerim Haji |
| author_facet | Abdukerim Haji |
| author_sort | Abdukerim Haji |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e83a102e049c4350a3b7067d365c5a50 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e83a102e049c4350a3b7067d365c5a502025-02-03T05:46:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/201682201682A Semigroup Approach to the System with Primary and Secondary FailuresAbdukerim Haji0College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaWe 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.http://dx.doi.org/10.1155/2010/201682 |
| spellingShingle | Abdukerim Haji A Semigroup Approach to the System with Primary and Secondary Failures International Journal of Mathematics and Mathematical Sciences |
| title | A Semigroup Approach to the System with Primary and Secondary Failures |
| title_full | A Semigroup Approach to the System with Primary and Secondary Failures |
| title_fullStr | A Semigroup Approach to the System with Primary and Secondary Failures |
| title_full_unstemmed | A Semigroup Approach to the System with Primary and Secondary Failures |
| title_short | A Semigroup Approach to the System with Primary and Secondary Failures |
| title_sort | semigroup approach to the system with primary and secondary failures |
| url | http://dx.doi.org/10.1155/2010/201682 |
| work_keys_str_mv | AT abdukerimhaji asemigroupapproachtothesystemwithprimaryandsecondaryfailures AT abdukerimhaji semigroupapproachtothesystemwithprimaryandsecondaryfailures |