• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권4호
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• 대한기계학회논문집B
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• 제26권5호
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• pp.695-702
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• 2002

Nonlinear dynamics of striped diffusion flames, by the diffusional-thermal instability with Lewis numbers sufficiently less than unity, is numerically investigated by examining various two-dimensional flame-structure solutions. The Lewis numbers for fuel and oxidizer are assumed to be identical and an overall single-step Arrhenius-type chemical reaction rate is employed in the model. Particular attention is focused on identifying the flame-stripe solution branches corresponding to each distinct stripe pattern and hysteresis encountered during the transition. At a Damkohler number slightly greater than the extinction Damkohler number, eight-stripe solution first emerges from one dimensional solution. The eight-stripe solution survives Damkohler numbers much smaller than the extinction Damkohler number until the transition to four-stripe solution occurs at the first forward transition Damkohler number. At the second forward transition Damkohler number, somewhat smaller than the first transition Damkohler number, the transition to two-stripe solution occurs. However, anu further transition from two-stripe solution to one-stripe solution is not always possible even if one-stripe solution can be independently accessed for particular initial conditions. The Damkohler number ranges for two-stripe and one-stripe solutions are found to be virtually identical because each stripe is an independent structure if distance between stripes is sufficiently large. By increasing the Damkohler number, the backward transition can be observed. In comparison with the forward transition Damkohler numbers, the corresponding backward transition Damkohler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.429-444
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• 2012

By using Mawhin continuation theorem and comparison theorem, the existence of periodic solution and persistence for a predator-prey system with diffusion and impulses are investigated in this paper. An example and simulation are given to show the effectiveness of the main results.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.295-309
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• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• 충청수학회지
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• 제10권1호
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• Journal of the Korean Wood Science and Technology
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• 제19권4호
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• pp.7-17
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• 1991

The feasibility of treating three softwood(Japanese larch pitch pine, and Korean pine) thinned logs by double-diffusion treatment processes was investigated. Some posts were incised before immersion, and others were imersed in hot copper sulfate solution. Comparison among species indicated that. in general, pitch pine was most treatable and Japanese larch least treatable. For all three species, almost all treatment schedules gave consistently good penetration and high net retention, but very steep gradient of preservative distribution. As expected, the treatability was increased by the extension of immersion time, increased concentration of treating solution, incising. and heating of the first solution. Of the variables tested, it appears that heating of the first solution is the most important. From the data in this paper, it may be concluded that, if the first solution is not heated, the best schedule is #3. If the first solution is healed. it appears the best schedules are #10 or #11. Since heating of the first solution improves the treatability. schedules # 10 or :#11 are recommended if the cost of heating might be justified. The data presented in this paper indicate that double-diffusion treatment processes seem to offer a promise as a comparatively effective and easy-operating method of treating thinned logs for the small-scale production of treated stock.

• Korean Membrane Journal
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• 제4권1호
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• pp.36-40
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• 2002

The diffusion coefficients of ions in the reverse transport system using the carrier mediated membrane were estimated from the diffusional membrane permeabilities and the ion activity in membrane system. In the aqueous alkali metal ions-membrane system diffusional flux of alkali metal ions driven by coupled proton was analyzed. The aqueous phase I contained NaOH solution and the aqueous phase II also contained NaCl and HCl mixed solution. The concentration of Na ions of both phases were $10^{0},\;10^{-1},\;10^{-2},\;5{\times}10^{-1}\;and\;5{\times}10^{-2}\;mol{\cdot}dm^{-3}$ and the concentration of HCI in aqueous phase II was always kept at $1{\times}10^{-1}\;mol{\cdot}dm^{-3}$. Moreover, the carrier concentration in liquid membrane was $10^{-2}\;mol{\cdot}dm^{-3}$. The results indicated that the diffusion coefficients depend strongly on the concentration of both phases electrolyte solution equilibriated with the membrane. The points were interpreted in terms of the energy barrier theory. Furthermore, eliminating the potential terms from the membrane equation was derived.

• 한국토양비료학회지
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• 제28권3호
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• pp.233-240
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• 1995

Ficks의 확산 편미방을 Laplace 변환을 적용하여 초기 및 경계조건과 함께 종속 대수 함수로 변환하고 Burington의 역변환표를 활용하여 복귀하는 방법으로 Ficks의 확산 편미방의 해를 구하였다. 적용된 초기 및 정계조건은 일정깊이의 담수에로 무한 깊이의 일정 염농도의 균일한 간척지 토양에서 상향 염분확산 이동에 대한 것이었다. 유도된 해는 특이 조건에서의 비교법으로 오.등 및 Kirkham, 등이 보고 한 간단한 초기 빛 경계조건에서의 해와 일치함을 확인했다. Ficks의 확산식의 해로 계산된 완만한 제염 속도를 근거로하여 담수 제염 방법별 제염 속도와 토양중 염분분포를 추정할수있는 모형식을 제시하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.31-40
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• 2009

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

• 공업화학
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• 제3권2호
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• pp.349-359
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• 1992

염료속에 함유된 무기염(NaCl, $Na_2SO_4$)의 선택적 제거를 위해 역확산과 역삼투를 결합한 방법과 nanofiltration(NF)을 각각 이용하였다. 역확산에 의한 염의 제거율은 염의 종류에 따라 1회(one pass)에 1~30%를 나타냈으며 염과 염료의 분리비는 10~500의 매우 큰 값을 갖는 반면 염료의 손실율은 0.3% 이하였다. 염료용액을 순환시킬수록 음이온인 $Cl^-$ 이온의 제거율이 증가하고 양이온인 $Na^+$ 이온의 제거율이 감소하는 도난투석현상이 관찰되었다. 또한 공급용액의 유속이 염의 제거에 미치는 영향을 살펴보았다. 역확산에 의해 염이 제거된 염료를 평판형 역삼투막을 사용하여 농축하였으며 $Cl^-$ 이온의 배제율을 solution-diffusion 모델식에 적용하였다 2회의 Diafiltration(DF)을 수행한 NF에서도 역확산에서와 마찬가지로 도난투석에 의해 $Cl^-$ 이온의 배제율 감소와 음배제율을 관찰하였다. 특히 두번째 DF에서 도난투석의 효과는 더욱 크게 나타났다.