ON THE SPECTRUM OF THE LINEAR TRANSPORT OPERATOR IN L~P SPACE

InthispaperweinvestigatethespectrumofthetransportoperatorA:Aam=Bac KegwhereBac=--aam(x,v,p)--vZ(x,v)op(x,v,p),Keg=11,joank(x,yip;V',p')op(x,v',p')dp'dy',D(A)={op(x,v,p)ELP(G):;;:t--:,y::op(a,v,--p)=0,for0相似文献   

WELL-POSEDNESS OF THE MODEL DESCRIBING A REPAIRABLE,STANDBY,HUMAN & MACHINE SYSTEM

By using the strong continuous semigroup theory of linear operators we provethe existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.     

ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.     

ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.