scholarly journals Asymptotic behavior of strongly monotone time-periodic dynamical processes with symmetry

1992 ◽  
Vol 100 (2) ◽  
pp. 355-378 ◽  
Author(s):  
Peter Takáč
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Processes ◽  
Strongly Monotone ◽  
Time Periodic

scholarly journals Mourre theory for time-periodic systems

1998 ◽  
Vol 149 ◽  
pp. 193-210 ◽  
Author(s):  
Koichiro Yokoyama
Keyword(s):  
Asymptotic Behavior ◽  
Adjoint Operator ◽  
The Self ◽  
Periodic Systems ◽  
Great Progress ◽  
Time Periodic ◽  
Commutator Method

Abstract.Studies for A.C. Stark Hamiltonian are closely related to that for the self-adjoint operator on torus. In this paper we use Mourre’s commutator method, which makes great progress for the study of time-independent Hamiltonian. By use of it we show the asymptotic behavior of the unitary propagator as σ → ± ∞.

ASYMPTOTIC BEHAVIOR OF SPATIALLY INHOMOGENEOUS BALANCE LAWS

2005 ◽  
Vol 02 (03) ◽  
pp. 645-672 ◽  
Author(s):  
JULIA EHRT ◽  
JÖRG HÄRTERICH
Keyword(s):  
Asymptotic Behavior ◽  
Vector Field ◽  
Initial Data ◽  
Periodic Solutions ◽  
Balance Laws ◽  
Spatially Inhomogeneous ◽  
Periodic Initial Data ◽  
Left And Right ◽  
Longtime Behavior ◽  
Time Periodic

We study the longtime behavior of spatially inhomogeneous scalar balance laws with periodic initial data and a convex flux. Our main result states that for a large class of initial data the entropy solution will either converge uniformly to some steady state or to a discontinuous time-periodic solution. This extends results of Lyberopoulos, Sinestrari and Fan and Hale obtained in the spatially homogeneous case. The proof is based on the method of generalized characteristics together with ideas from dynamical systems theory. A major difficulty consists of finding the periodic solutions which determine the asymptotic behavior. To this end we introduce a new tool, the Rankine–Hugoniot vector field, which describes the motion of a (hypothetical) shock with certain prescribed left and right states. We then show the existence of periodic solutions of the Rankine–Hugoniot vector field and prove that the actual shock curves converge to these periodic solutions.

ESTIMATING DISCRETE-TIME PERIODIC SOFTWARE REJUVENATION SCHEDULES UNDER COST EFFECTIVENESS CRITERION

2006 ◽  
Vol 13 (06) ◽  
pp. 565-579
Author(s):  
KAZUKI IWAMOTO ◽  
TADASHI DOHI ◽  
NAOTO KAIO
Keyword(s):  
Asymptotic Behavior ◽  
Cost Effectiveness ◽  
Discrete Time ◽  
Parametric Method ◽  
Regenerative Process ◽  
Numerical Examples ◽  
Software Aging ◽  
Software Rejuvenation ◽  
Markov Regenerative Process ◽  
Time Periodic

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider the similar periodic software rejuvenation model to Garg et al.13 under the different operation circumstance. That is, we model the stochastic behavior of telecommunication billing applications by using a discrete-time Markov regenerative process, and determine the optimal periodic software rejuvenation schedule maximizing the so-called cost effectiveness, in discrete-time setting. Also, we provide a statistically non-parametric method to estimate the optimal software rejuvenation schedule, based on the discrete total time on test concept. Numerical examples are devoted to illustrate the determination/estimation of the optimal software rejuvenation schedule and to examine the asymptotic behavior of the estimator developed here.

Sign in / Sign up

Export Citation Format

Share Document