| Abstract: | The time-dependent solution of a kind of supply chain system with the multi-suppliers and single demander is investigated in this paper. By choosing state space and defining operator of system, we transfer model into an abstract Cauchy problem. We are devoted to studying the unique existence of the system solution and its exponential stability by using the theory of C_0-semigroup. We prove that the system operator generates C_0-semigroup by the theory of cofinal operator and resolvent positive operator. We derive that the system has a unique nonnegative dynamic solution exponentially converging to its steady-state one which is the eigenfunction corresponding eigenvalue 0 of the system operator. |
