• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.281-294
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• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.66-71
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• 1988

Let B be present value of some sequence. This paper concerns the maximization of the expected utility of the present value B when the utility function is exponential.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.4
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• pp.109-116
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• 1988

This study was aimed at determining a regime of flow through rubble mound dike consisted of all sized quarrystons, and deriving a relationship between hydraulic gradient (I) and mean flow velocity (V) through the dike. The analysis was carried out with the data observed after final gap closing of the Haenam Sea dike from May, 6 to May, 14, 1987. The resu]ts are summarized as follows: 1. The regime of flow would be defined as the turbulent flow. 2. As to the relationships, two kinds of formula that are exponential and binomial were obtained. Exponential formula: I=2.099V 1.2888 Binomial formula: I=0.6113V+5.5235V$^2$ 3. Correlation coefficient of the former was 0.824 and that of the latter was 0.821, and the deviations between observed data and estimated were 0.0070 and 0.0064 respectively. 4. Comparing the correlation coefficient, both the equations have the same correlation coefficients, but in case of the deviation the binomial equation was better than the exponential equation. Therefore, the binomial equation is proposed for analyzing the flow through rubble mound dike.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.859-888
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• 2021

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

• ETRI Journal
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• v.31 no.1
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• pp.42-50
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• 2009

A new method for simulating voltage and current distributions in transmission lines is described. It gives the time domain solution of the terminal voltage and current as well as their line distributions. This is achieved by treating voltage and current distributions as distributed state variables (DSVs) and turning the transmission line equation into an ordinary differential equation. Thus the transmission line is treated like other lumped dynamic components, such as capacitors. Using backward differentiation formulae for time discretization, the DSV transmission line component is converted to a simple time domain companion model, from which its local truncation error can be derived. As the voltage and current distributions get more complicated with time, a new piecewise exponential with controllable accuracy is invented. A segmentation algorithm is also devised so that the line is dynamically bisected to guarantee that the total piecewise exponential error is a small fraction of the local truncation error. Using this approach, the user can see the line voltage and current at any point and time freely without explicitly segmenting the line before starting the simulation.

• Korea-Australia Rheology Journal
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• v.16 no.2
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• pp.57-62
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• 2004

Turbulent drag reduction (DR) efficiency of water soluble poly(ethylene oxide) (PEO) with two different molecular weights was studied as a function of polymer concentration and temperature in a turbulent flow produced via a rotating disk system. Its mechanical degradation behavior as a function of time in a turbulent flow was also analyzed using both a simple exponential decay function and a fractional exponential decay equation. The fractional exponential decay equation was found to fit the experimental data better than the simple exponential decay function. Its thermal degradation further exhibited that the susceptibility of PEO to degradation increases dramatically with increasing temperature.

• Journal of Korean Society of Water and Wastewater
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• v.16 no.6
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• pp.710-716
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• 2002

A General Pipe Break Prediction Model that incorporates linear and exponential models in its form is developed. The model is capable of fitting pipe break trends that have linear, exponential or in between of linear and exponential trend by using a weighting factor. The weighting factor is adjusted to obtain a best model that minimizes the sum of squared errors of the model. The model essentially plots a best curve (or a line) passing through "cumulative number of pipe breaks" versus "break times since installation of a pipe" data points. Therefore, it prevents over-predicting future number of pipe breaks compared to the conventional exponential model. The optimal replacement time equation is derived by using the Threshold Break Rate equation by Loganathan et al. (2002).

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.47-51
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• 2001

We establish the global existence of nonnegative solutions to some reaction-diffusion equation for exponential nonlinearity for small initial data.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.145-156
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• 2008

When we consider a life insurance company that sells a large number of continuous T-year term life insurance policies, it is important to find an optimal strategy which maximizes the surplus of the insurance company at time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy which maximizes the expected exponential utility of the final value of the surplus at the end of T-th year. To do this we solve the corresponding Hamilton-Jacobi-Bellman equation.