• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• East Asian mathematical journal
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• 제39권3호
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• pp.319-329
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• 2023

In this paper, we consider a stochastic higher-order Kirchhoff-type equation with nonlinear damping and source terms. We prove the blow-up of solution for a stochastic higher-order Kirchhoff-type equation with positive probability or explosive in energy sense.

• 대한수학회논문집
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• 제24권1호
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• pp.85-97
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• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• 충청수학회지
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• 제35권2호
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• pp.137-147
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• 2022

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.260-277
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• 2021

The appropriate radiation conditions of ship motion problem with advancing speed in frequency domain are investigated from a theoretical and practical point of view. From extensive numerical experiments that have been conducted for evaluation of the relevant radiation conditions, a hybrid radiation technique is proposed in which the Sommerfeld radiation condition and the free surface damping are mixed. Based on the comparison with the results of the translating and pulsating Green function method, the optimal damping factor of the hybrid radiation technique is selected, and the observed limitations of the proposed hybrid radiation technique are discussed, along with its accuracy obtained from the numerical solutions. Comparative studies of the forward-speed seakeeping prediction methods available confirm that the results of applying the hybrid radiation technique are relatively similar to those obtained from the translating and pulsating Green function method. This confirmation is made in comparisons with the results of solely applying either the free surface damping, or the Sommerfeld radiation condition. By applying the proposed hybrid radiation technique, the wave patterns, hydrodynamic coefficients, and motion responses of the Wigley III hull are finally calculated, and compared with those of model tests. It is found that, in comparison with the model test results, the three-dimensional Rankine source method adopting the proposed hybrid radiation technique is more robust in terms of accuracy and numerical stability, as well as in obtaining the forward speed seakeeping solution.

• Journal of Power Electronics
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• 제18권4호
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• pp.1178-1189
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• 2018

In grid-connected voltage-source inverters (VSIs), when compared with a simple inductive L filter, the LCL filter has a better performance in attenuating the high frequency harmonics caused by the pulse-width modulation of power switches. However, the resonance peaks generated by the filter inductors and capacitors can make a system unstable. In terms of simplicity and filter design cost, a passive damping method is generally preferred. However, its high power loss and degradation in high frequency harmonic attenuation are significant demerits. In this paper, a mathematical design solution for a passive LCL filter to derive filter parameters suppressing the high frequency current harmonics to 0.3% is proposed. The minimum filter inductance can be obtained to reduce the size of the filter. Furthermore, a minimum damping resistance design considering a current controller is analyzed for a stable closed-loop system. The proposed design method is verified by experimental results using a 5-kW three-phase prototype inverter.

• Journal of Mechanical Science and Technology
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• 제15권3호
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• pp.392-402
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• 2001

The paper reports a multiple source modeling of low-Reynolds-number dissipation rate equation with aids of DNS data. The key features of the model are to satisfy the wall limiting conditions of the individual source terms in the exact dissipation rate equation using the wall damping functions. The wall damping functions are formulated in term of dimensionless dissipation length scale ι(sup)+(sub)D(≡ι(sub)D($\upsilon$$\xi$)(sup)1/4/$\upsilon$) and the invariants of small and large scale turbulence anisotropy tensors. $\alpha$(sub)ij(=$\mu$(sub)i$\mu$(sub)j/$\kappa$-2$\delta$(sub)ij/3) and e(sub)ij(=$\xi$(sub)ij/$\xi$-2$\delta$(sub)ij/3). The model constants are optimized with aids of DNS data in a plane channel flow. Adopting the dissipation length scale as a parameter of damping function, the applicabilities of $\kappa$-$\xi$ model are extended to the turbulent flow calculation of complex flow passages.

• 대한수학회지
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• 제59권1호
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• pp.205-216
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• 2022

This paper deals with a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. This work is devoted to prove a global nonexistence of solutions for a nonlinear wave equation with nonnegative initial energy as well as negative initial energy.

• East Asian mathematical journal
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• 제32권3호
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• pp.377-385
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• 2016

Global attractor is a basic concept to study the long-time behavior of solutions of the various equations. This paper is investigated with the existence of a global attractor for the beam equation $$u_{tt}+{\Delta}^2u-{\nabla}{\cdot}\{{\sigma}({\mid}{\nabla}u{\mid}^2){\nabla}u\}+f(u)+a(x)g(u_t)=h,$$ using multipliers technique and Nakao's Lemma.

• KSTLE International Journal
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• 제9권1_2호
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• pp.1-6
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• 2008

In this study is performed a complex lubrication analysis of a herringbone groove air journal bearing, which shows a big potential as an oilless bearing for a color wheel used as an original color source for a large DLP projection television and rotating at a rated-speed of 10,800 rpm. The Galerkin FE and perturbation methods are used for a lubrication analysis of the bearing. The effects of groove number, angle and depth and bearing clearance on the dynamic stability of the bearing are investigated in terms of the critical mass, and its equilibrium positions, stiffness and damping coefficients are calculated at various rotating speeds. Results have shown that the designed herringbone groove air journal bearing is quite suitable as a support bearing for the considered high-speed color wheel in terms of the complex lubrication performances of the bearing itself.