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Semigroup Approach to the Gaver`s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations
阿不都克热木·阿吉 教授(新疆大学)
2018-01-01 12:13  华东师范大学

报告摘要:We investigate Gaver`s parallel system attended by a cold standby unit and a repairman with multiple vacations. We first prove the existence of a unique dynamic solution of the system by using $C_0-$semigroup theory for linear operators. Then by analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we show that the dynamic solution converges strongly to the steady state solution which is the eigenfunction corresponding to eigenvalue $0$ of the system operator. Thus we obtain the asymptotic stability of the dynamic solution of this system.