• 대한기계학회논문집
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• 제18권1호
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• pp.150-155
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• 1994

An Approximate solution for plane two-dimensional incompressible laminar jet issuing from a finite opening with arbitrary initial profile into the same ambient fluid is proposed. For an arbitrary initial velocity profile, the problem is generated from the well known similarity solution for the jet of infinitesimal opening and provides good approximations in the region where the similarity solution cannot be used as an approximation. The asymptotic behavior of this solution is investigated and it is shown that, as goes downstream, the present solution approachs the similarity solution.

• 대한수학회보
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• 제55권4호
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• 대한수학회보
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• 제50권3호
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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 ${\phi}=0$.

• Geomechanics and Engineering
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• 제25권4호
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• pp.303-315
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• 2021

A rigorous and generic similarity solution is developed for assessment of the undrained expansion responses of a cylindrical cavity expansion in K₀-consolidated anisotropic soils. A K₀-consolidated anisotropic modified Cam-clay (K₀-AMCC) model that can represent the initial stress anisotropy and the effects of stress-induced anisotropy is used to model the soil behaviors during cavity expansion. All the seven basic unknowns, the three stress components, the pore water pressure, the particle velocity, the specific volume and the hardening parameter, are reduced to the functions of a dimensionless radial coordinate and are taken as coupled variables to formulate the problem. The governing equations are formulated by making use of the equilibrium equation, the constitutive equation, the consistency condition, the continuity condition and the undrained condition, which are then solved as an initial value problem. The proposed rigorous similarity solution is compared with some well-documented rigorous solutions to validate the solution and to highlight the special expansion responses in anisotropic soils. The results reveal that the present solution can yield more predictions for cavity expansion problems in soils with initial anisotropic stresses.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.693-698
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• 2019

In this study, the problem of axisymmetric deformation of prestressed $F{\ddot{o}}ppl-Hencky$ membrane under constrained deflecting was analytically solved and its closed-form solution was presented. The small-rotation-angle assumption usually adopted in membrane problems was given up, and the initial stress in membrane was taken into account. Consequently, this closed-form solution has higher calculation accuracy and can be applied for a wider range in comparison with the existing approximate solution. The presented numerical examples demonstrate the validity of the closed-form solution, and show the errors of the contact radius, profile and radial stress of membrane in the existing approximate solution brought by the small-rotation-angle assumption. Moreover, the influence of the initial stress on the contact radius is also discussed based on the numerical examples.

• Korean Journal of Mathematics
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• 제5권2호
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• pp.151-167
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• 1997

We estimate the interior Lipschitz norm and maximum of the solution for degenerate parabolic equations with absorption. Also obtain the growth rate of the solution $u$ in terms of time $t$. From this we show the uniqueness of solution with respect to the initial trace.

• 한국지능시스템학회논문지
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• 제11권8호
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• pp.715-719
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• 2001

본 논문에서는 E$^{2}$$_{N}$상에서 비국소 초기 조건을 갖는 비선형 퍼지 미분방정식에 대한 퍼지해의 존재성과 유일성에 관한 연구이다.

• 한국국방경영분석학회지
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• 제26권1호
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• pp.47-55
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• 2000

The purpose of this paper is to develop a new heuristic algorithm for vehicle routing problem. The algorithm is composed of two steps. First step is to make a initial solution using sweeping algorithm. Second step is to improve initial solution for optimal solution using node exchange algorithm and tabu search algorithm. We have proven that our algorithm has produced better results than solutions obtained by saving algorithm and genetic in ten example problems with different unit size.

• Journal of Advanced Marine Engineering and Technology
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• 제40권10호
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• pp.888-893
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• 2016

In this study, the solution plasma process was utilized with the aim of degrading synthetic dyes in water at atmospheric pressure. The experiments were conducted in a batch-type reactor consisting of a symmetric wire-wire electrode configuration with rhodamine B (RhB) as the target synthetic dye. The effects of the plasma treatment time and initial dye concentration on the RhB degradation were investigated by monitoring the change in absorbance of RhB solutions. The RhB solutions turned lighter in color and finally colorless with prolonged plasma treatment time, indicating the destruction of dye molecules. The RhB solutions were found to have degraded, following the first-order kinetic process. However, for high initial RhB concentrations, another kinetic process or factor seems to play a dominant role at the initial degradation stage. The fitted first-order rate constant decreased as the initial concentration increased. This result suggests that the degradation behavior and kinetic process of the RhB solution strongly depends on its initial concentration. The RhB degradation is considered to be due to a combination of factors, including the formation of chemically oxidative species, as well as the emission of intense UV radiation and high-energy electrons from the plasma. We believe that the solution plasma process may prove to be an effective and environment-friendly method for the degradation or remediation of synthetic dye in wastewater.

• Environmental Engineering Research
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• 제25권3호
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• pp.316-323
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• 2020

The degradation of aqueous oxytetracycline (OTC) from an aqueous solution antibiotic using H₂O₂/Fe²⁺ process was studied in one 1 L batch chemical reactor. The extent of OTC degradation (20 mg/L) was investigated from a known initial pH solution, temperature and the type of catalyst (Fe²⁺, Fe³⁺) and for various initial concentrations of OTC, H₂O₂ and Fe²⁺. The degradation efficiency achieved was found to be very important (90.82% and 90.63%) at initial pH solution of 3 and 4, respectively. However, the type of catalyst and the reaction temperature had a slight impact on the final degradation of OTC. The results showed that the OTC removal increased with increasing initial H₂O₂ concentration in the range of 70 to 150 mg/L and initial Fe²⁺ concentrations in the range of 2 to 5 mg/L. The highest degradation efficiency obtained at ambient temperature was 90.95% with initial concentration of OTC of 10 mg/L, H₂O₂ = 150 mg/L and Fe²⁺ = 5 mg/L. Moreover, biodegradability improved from 0.04 to 0.36 and chemical oxygen demand degradation was 78.35% after 60 min of treatment. This study proved that Fenton process can be used for pretreatment of wastewater contaminated by OTC before a biological treatment.