Exponential Asymptotic Property Of The Solution Of The Repairable System With Warm Standby Wiht Two Same Parts

This dissertation collects the main results obtained by the author during the period when she has applied for the M.D.Chapter 1 simply reviews current status of researching of the repairable system in both home and abroad and introduces some definitions and theorys.Chaper 2 is to introduce the mathmatics model of the repairable system with warm standby with two same parts,which can be described by a group of partial differential equations with integral boundary conditions.By dynamically studying this system on the base of the mathematical model,we define the Banach space on the fact of physics background,then we can obtain the unique existence and the well-posedness of solution of the system by using the knowledge of C₀ semigroup theory.Chapter 3 is devoted to asymptotic behavior of the solution of the system by analyzing the spectrum of the system and some knowledge of C₀ semigroup stability theory.Chapter 4 discusses the main object of this paper to solve the convergence rate of the time-dependent solution of the system,which tends to the steady-state solution as time tends to infinite.By mainly using the knowledge of the quasi-compact semigroup, we get the convergence rate is exponential.Chapter 5 discusses the availability,one of the most important indexs of the system reliability,which can be obtained by normalizing the stable solution of the system.