A Semigroup Approach to the System with Primary and Secondary Failures

Abstract EN

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.