A Semigroup Approach to the System with Primary and Secondary Failures - Abdukerim Haji (International Journal of Mathematics and Mathematical Sciences)
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.