• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.157-164
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• 2000

This paper discusses the error propagation characteristics of the Newmark explicit method, modified Newmark explicit method and ${\alpha}$-function dissipative explicit method in pseudodynamic tests. The Newmark explicit method is non-dissipative while the ${\alpha}$-function dissipative explicit method and the modified Newmark explicit method are dissipative and can eliminate the spurious participation of high frequency responses. In addition, error propagation analysis shows that the modified Newmark explicit method and the ${\alpha}$-function dissipative explicit method possess much better error propagation properties when compared to the Newmark explicit method. The major disadvantages of the modified Newmark explicit method are the positive lower stability limit and undesired numerical dissipation. Thus, the ${\alpha}$-function dissipative explicit method might be the most appropriate explicit pseudodynamic algorithm.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-107
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• 2012

The concept of Hilbert space dissipative norm was introduced in [8] to obtain necessary and sufficient conditions for exponential stability of contraction semigroups. In the present paper we show that the same concept can also be used to derive further properties of contraction semigroups, as well as to characterize strongly stable semigroups that are not exponentially stable.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.11
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• pp.1598-1604
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• 2015

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.151-162
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• 2017

Two $Chang-{\alpha}$ dissipative family methods and two $KR-{\alpha}$ family methods were developed for time integration recently. Although the four family methods are in the category of the dissipative structure-dependent integration methods, their performances may be drastically different due to the detrimental property of weak instability or overshoot for the two $KR-{\alpha}$ family methods. This weak instability or overshoot will result in an adverse overshooting behavior or even numerical instability. In general, the four family methods can possess very similar numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and controllable numerical damping. However, the two $KR-{\alpha}$ family methods are found to possess a weak instability property or overshoot in the high frequency responses to any nonzero initial conditions and thus this property will hinder them from practical applications. Whereas, the two $Chang-{\alpha}$ dissipative family methods have no such an adverse property. As a result, the performances of the two $Chang-{\alpha}$ dissipative family methods are much better than for the two $KR-{\alpha}$ family methods. Analytical assessments of all the four family methods are conducted in this work and numerical examples are used to confirm the analytical predictions.

• Polymer(Korea)
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• v.25 no.4
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• pp.536-544
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• 2001

We investigate, in the viewpoint of mathematical stability, the validity of the time-strain separability hypothesis employed in polymer viscoelasticity on the basis of experimental results. There have been suggested two distinct stability criteria such as Hadamard related to quick response and dissipative stability conditions, and in the limit of high deformation rate we have proved that separable constitutive equations are either Hadamard or dissipative unstable. The fact that the separability is not valid in the short time region in stress relaxation experiments exactly coincides with the results of our analysis. Therefore, since the application of the separability hypothesis incurs thermodynamic inconsistency as well as mathematical instability, such application should be avoided in the formulation of constitutive equations. In addition, careful attention should be paid to the limit of its validity even in experiments. It is also proved that there is neither theoretical nor physical validity of using the damping function.

• The Korean Journal of Rheology
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• v.7 no.3
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• pp.192-202
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• 1995

이연구에서는 유변학 구성방정식이 나타내는 일차원 불안정성의 몇가지 예를 보였 다. 안정성 해석을 위하여 맥스웰형 미분구성방정식 Giesekus, Leonov, Larson 모델을 선택 하였다. 나타난 불안정성은 단순전단유동에서의 정상유동곡석이 무제한적 단수증가성을 위 배할 때 발생한다. 단순전단유동에 부과된 섭동하에서 Giesekus와 Larson 모델이 일정영역 의 무델계수와 전단율속도값에서 불안정 거동은 관성력을 고려하지 않은 경우에도 발생함이 증명되었다. 끝으로 이러한 불안정 거동을 개선하는 몇가지 방법을 Leonv와 Giesekus 모델 에 대하여 제시하였다.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.869-876
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• 1995

Piezo devices such as piezoceramic patches knwon as collocated rate sensor and actuators are commonly used in control of flexible structure (see, e.g., [1]) and noise reduction. Recently, Ito and Kang ([4]) developed a nonlinear feedback control synthesis for regulating fluid flow using these devices.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.81-87
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• 1993

In this paper robust stability conditions are obtained for linear dynamical systems under structured nonlinear time-varying perturbations, using absolute stability theory and the concept of dissipative systems. The conditions are expressed in terms of solutions to linear matrix inequality(LMI). Based on this result, a synthesis methodology is developed for robust feedback controllers with worst-case H$_{2}$ perforrmance via convex optimization and LMI formulation.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.17-26
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• 2002

A stability analysis of a non-linear prey-predator system under the influence of one dimensional diffusion has been investigated to determine the nature of the bifurcation point of the system. The non-linear bifurcation analysis determining the steady state solution beyond the critical point enables us to determine characteristic features of the spatial inhomogeneous pattern arising out of the bifurcation of the state of the system.