• East Asian mathematical journal
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• v.34 no.5
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• pp.633-641
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• 2018

A viscoelastic wave equation in canonical form weakly nonlinear time dependent dissipation and source terms is investigated in this paper. And we establish a general decay result which is not necessarily of exponential or polynomial type.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.681-689
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• 2014

In this paper, we investigate the influence of boundary dissipations on decay property of the solutions for a semilinear wave equation with damping and memory condition on the boundary using the multiplier technique.

• East Asian mathematical journal
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• v.32 no.5
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• pp.651-658
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• 2016

In a bounded domain, we consider $$u_{tt}-{\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;g(t-{\tau}){\Delta}ud{\tau}+u_t={\mid}u{\mid}^pu$$, where p > 0 and g is a nonnegative and decaying function. We establish a general decay result which is not necessarily of exponential or polynomial type.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1433-1448
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• 2021

In the present work, we investigate a viscoelastic equation involving a logarithmic nonlinear source term. After proving the existence of solutions, we establish a general decay estimate of the solution using energy estimates and theory of convex functions. This result extends and complements some previous results of [9, 21].

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.5
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• pp.538-542
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• 2015

The transverse moment of inertia is an indispensable factor in analyzing the roll motion characteristics of ships and the calculating method needs to be based on the more reasonable theories when deciding the value as the results and reliability of analysis could be much affected by the correctness. However, the mass distribution and shape of hulls are quite complicated and give much difficulties in case of calculating the value directly from the ship design data, furthermore even acquiring the detailed design data for calculation is almost impossible. Therefore some simpler ways are practically adopted in the assumption that the gyradius of roll moment can be decided by a given ratio and hull width. It is well known that the responses of the free roll decay are varied according to the value of roll moment in view of roll period and amplitude decay ratio, so that the general formula to get the moment value can be derived also from the observation of roll decay responses. This study presents how the roll period and decay ratio are interrelated each other from the roll motion characteristics with suggesting a general formula to be able to calculate roll moment from it. Finally, the obtained general formula has been applied to a ship data to check the resultant characteristics through analyzing graphs and showed that the roll moment becomes more accurate when rolling period and decay ratio are considered together in calculation.

• 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.

• Journal of the Korean Wood Science and Technology
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• v.24 no.1
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• pp.81-86
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• 1996

This study was performed to evaluate the reduction in bending properties of radiata pine sapwood associated with incipient brown-rot decay. Decayed bending specimens by Tyromyces palustris and Gloeophyllum trabeum for varoious periods were tested destructively. Brown-rot decay by T. palustris and G. trabeum caused serious reduction in bending properties at very early stages of decay, with about 30 percent decrease in bending strength observed for only 1~2 percent weight loss. In general, the reduction in bending properties caused by T. palustris was somewhat greater than that by G. trabeum. Work to maximum load was reduced most severely and rapidly from the onset of decay, while modulus of elasticity showed a much more moderate rate of reduction. Modulus of rupture was affected by decay to a greater extent than was modulus of elasticity. Since a relatively strong correlation between weight loss and bending strength was observed, the residual strength of decayed wood can be predicted by weight loss due to decay. The results of this study indicate that very early stages of brown-rot decay reduce the bending strength significantly. Thus, it is recommended that all load-bearing members in wooden structures, especially those that are periodically wetted, should be inspected regularly to prevent a sudden failure even though there are no definite signs of decay.

• Journal of the Korean Regional Science Association
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• v.31 no.2
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• pp.47-61
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• 2015

The purpose of this study to empirical analysis of the effects of distance-decay for the relocated firms in the Seoul Metropolitan Area(SMA). In addition, this study was constructed distance-decay function for the relocated firms by industrial types using a general distance-decay function. The data of relocated firms in the SMA extracted from the spatial database which was constructed in an previous research. The industrial type divided into 3 parts which are construction, manufacturing, and service. The result of empirical analysis by each industrial type of the effect of distance-decay, the explanatory power($R^2$) of the each function were all high. In the construction, the adjusted $R^2$ of the distance-decay function was 0.728, the manufacturing was 0.802 and the service was 0.812. It means the effect of distance decay for the relocated firms in construction industrial type more big than the effects of distance decay for the manufacturing and service industrial types.

• Journal of the Korean housing association
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• v.20 no.2
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• pp.109-118
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• 2009

In general, the decay of the residential district has been considered a phenomenon of old towns. But now it has become a problem of new development areas too, which have been a cause of the decay of old town. This study aims to investigate the decay of the residential district in the new development area. The survey site was Dunsan, a town-intown of Daejeon metropolitan city. The findings were as follows (:) 1) even in the new development area, a high level of vacancy ratio was evident. ; 2) among the buildings above ground, 1st floor showed the highest vacancy ratio, which means the 1st floor was allotted to too many commercial facilities relative to the buying power size in this district. ; 3) there were many conversions in response to the decay of the district, from residential to commercial, and commercial to residential. ; and 4) the allocation of each type of conversion showed a spatial pattern.