Open Access Open Access  Restricted Access Subscription or Fee Access

Semigroup Method for a System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity

Abdukerim Haji


We investigate a system consisting of a reliable machine, an unreliable machine and a storage buffer with nite capacity. This system can be described by a group of partial dierential equations with integral boundary conditions. By using C0_semigroup theory of functional analysis, we prove the well-posedness and the existence of a unique positive dynamic solution of the system. And then through analyzing the spectra distribution of the system operator and irreducibility of the semigroup generated by the system operator, we deduce that the dynamic solution converges strongly to steady state solution, thus we obtain the asymptotic stability of the dynamic solution.


C0-semigroup, dynamic solution, well-posedness, asymptotic stability.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.