Study On The Dynamic Solution Of An N-unit Series System With Finite Number Of Vacations

This thesis is divided into four parts.The first part is the introduction,which consists of the research background,the research methods and the basic ideas of research.The second part introduces N unit series system with finite number of vacations and its mathematical model.The third part firstly rewrites the mathematical model of N unit series system with finite number of vacations as an abstract Cauchy problem in a suitable Banach space,and then proves that zero is an eigenvalue of the system operator and all points on the imaginary axis except zero belong to the resolvent set of the operator,finally,proves that the system operator generates a positive contraction C0-semigroup,and thus obtain the existence and uniqueness of positive dynamic solution of the system.The fourth part firstly study irreducibility of the semigroup generated by the system operator,and then we prove that the dynamic solution converges to its static solution in the sense of norm by using the spectral distribution of the system operator and the irreducibility of the semigroup generated by the system operator,thus obtain the asymptotic stability of the dynamic solution of the system.