We investigate the solution of an N-unit series system with finite number of vacations. By using CC00-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

Article history: Received 31 August 2015 Available online 27 February 2016 MSC: 35B34 35B35 35B40 35J05 78A25

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