• 대한수학회보
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• 제61권1호
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• pp.161-193
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• 2024

In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term h ∈ L²_b(ℝ; H^-1(ℝ^N)) is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor A, i.e., A is a bounded subset of H²(ℝ^N) × H¹(ℝ^N) × L²_µ(ℝ⁺, H²(ℝ^N)). The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.

• 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.

• International Journal of Computer Science & Network Security
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• 제22권6호
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• pp.91-96
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• 2022

The photocatalytic degradation of salicylic acid takes place in several stages involving coupled phenomena, such as the transport of molecules and the chemical reaction. The systems of transport equations and the photocatalytic reaction are numerically solved using COMSOL Mutiphysics (CM) simulation software. CM will make it possible to couple the phenomena of flow, the transport of pollutants (salicylic acid) by convection and diffusion, and the chemical reaction to the catalytic area (bauxite or TiO2 doped by nanoparticles). The simulation of the conversion rate allows to correctly fit the experimental results. The temporal simulation shows that the reaction reaches equilibrium after a transitional stage lasting over one minute. The outcomes of the study highlight the importance of diffusion in the boundary layer and the usefulness of injecting micro-agitation into the microchannel flow. Under such conditions, salicylic acid degrades completely.

• 폴리머
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• 제24권1호
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• pp.105-112
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• 2000

본 연구에서는 항공기 구조용 재료로 쓰이는 탄소섬유/에폭시 복합재료 프리프레그(DMS 2224)를 모델시스템으로 하여 등온환경과 등속도 가열환경에서 경화반응 속도를 연구하였다. 이 복합재료의 공정온도에서의 가공공정을 묘사할 수 있는 현상학적인 반응속도 모델을 differential scanning calorimetry (DSC)와 이론을 통하여 제안하였다. 등온환경에서의 실험으로부터 반응특성곡선을 관찰한 결과 경화반응이 1차 반응함수임을 확인하였고, 활성화 에너지는 78.43 kJ/mo1을 얻었다. 이 프리프레그는 경화온도에 따라 한계경화도를 보여주어 유리화가 존재함을 확인하였고 이를 1차 반응속도 모델에 적용시킨 결과, 유리화 이후의 확산우세현상을 포함한 반응속도 모델을 제안하였다. 제안된 모델식을 이용하여 등온/등속도 가열환경을 포함한 실제 경화공정을 성공적으로 표현할 수 있었다.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.39-43
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• 1996

Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• 대한수학회지
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• 제47권1호
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• pp.165-187
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• 2010

We introduce two numerical schemes for solving a system of ordinary differential equations which characterizes several kinds of linear reactions and diffusion from biochemistry, physiology, etc. The methods consist of sequential applications of the simple exact solver for a reversible reaction. We prove absolute stability and convergence of the proposed explicit methods. One is of first order and the other is of second order. Numerical results are included.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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• pp.7-20
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• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.

• 전기화학회지
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• 제15권3호
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• pp.165-171
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• 2012

본 연구에서는 전기화학계에서 중요한 다중전자의 이동이 수반되는 전극 반응에 대하여 순환전위법의 특성곡선을 모델링하여, MATLAB 프로그램으로 구현하였다. 전극주변의 전기화학 물질전달계에 대하여 반무한 확산모델의 경계조건을 설정하였고, Fick의 농도방정식은 유한차분법으로 전개하여 수치해를 구하였고, Butler-Volmer 식으로부터 계산된 농도값을 전류의 값으로 전환하였다. 본 연구에서 구현된 수치해는 기존의 실험치들과 합리적으로 설명하고 있었으며, 이를 근거로 다중전자 전기화학 반응계에서 반응메카니즘에 대한 전극반응속도 상수와 CV 주사속도 영향을 효과적으로 해석할 수 있었다.

• Nuclear Engineering and Technology
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• 제50권6호
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• pp.915-922
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• 2018

Metallic fuel has been considered for sodium-cooled fast reactors because it can maximize the uranium resources. It generates rare earth elements as fission products, where it is reported by aggravating the fuel-cladding chemical interaction at the operating temperature. Rare earth elements form a multicomponent alloy (Ce-Nd-Pr-La-Sm-etc.) during reactor operation, where it shows a higher reaction thickness than a single element. Experiments have been carried out by simplifying multicomponent alloys for mono or binary systems because complex alloys have difficulty in the analysis. In previous experiments, xCe-yNd was fabricated with two elements, Ce and Nd, which have a major effect on the fuel-cladding chemical interaction, and the thickness of the reaction layer reached maximum when the rare earth elements ratio was 1:1. The objective of this study is to evaluate the effect and relationship of rare earth elements on such synergistic behavior. Single and binary rare earth model alloys were prepared by selecting five rare earth elements (Ce, Nd, Pr, La, and Sm). In the single system, Nd and Pr behaviors were close to diffusion, and Ce showed a eutectic reaction. In the binary system, Ce and Sm further increased the reaction layer, and La showed a non-synergy effect.