• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.43-54
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• 2014

This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato's approximating approach, existence and uniqueness of strong solutions are obtained.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.379-403
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• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.327-342
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• 2007

In this paper, a kind of pest-predator model with impulsive effect and infinite delay is considered by the method of chain transform. By using Floquet's theorem, it is shown that there exists a globally asymptotically stable periodic pest eradication solution when the impulsive period is less than or equal to some critical value which is a directly proportional function with respect to the population of release. Furthermore, it is proved that the system is permanent if the impulsive period is larger than some critical value. Finally, the results of the corresponding systems are compared, those results obtained in this paper are confirmed by numerical simulation.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.4
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• pp.703-707
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• 1989

The ignition of solid particle under strong convective heating has been investigated by applying an asymptotic analysis to a semi-infinite body for varying values of gas recovery temperature and convective heat transfer coefficient. It was found that if the scale of the reaction zone is much smaller than the characteristic length of the body size, then infinite body theory can be used to estimate the ignition delay time. Furthermore, the convective heat transfer coefficient was found to have more influence on predicting the ignition delay times of particle exposed to an incident shock wave rather than the gas recovery temperature.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.1-14
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• 2020

Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.457-466
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• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.101-112
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• 2007

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability of abstract neutral functional integrodifferential systems with infinite delay. As application, an example is provided to illustrate the obtained results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1678-1685
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• 1993

This paper considers a time delay control of noncolocated flexible mechanical systems in discrete time domain. A stability criterion suggested in the previous paper is,extended in the consideration of infinite mode property of flexible systems and finite control sampling frequency. Based on the stability criterion, the one step advanced discrete time derivative control is suggested, which can stabilize infinite number of modes of a flexible system. The sensitivity analysis shows the robustness of the one step advanced control to the system parameter uncertainties and time delay errors. Application to a simply supported beam verifies the extended stability criterion and the effectiveness of the one step advanced D-control.