• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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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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• v.22 no.6
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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.

• Polymer(Korea)
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• v.24 no.1
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• pp.105-112
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• 2000

Using a commercial epoxy/carbon fiber composite prepreg (DMS 2224) as a model system, the cure kinetics of vitrifying thermoset system were analyzed by isothermal and dynamic-heating experiments. Focusing on the processing condition of high performance composite systems, a phenomenological kinetic model was developed by using differential scanning calorimetry (DSC) and reaction kinetics theories. The model system exhibited a limited degree of cure as a function of isothermal temperature seemingly due to the diffusion-controlled reaction rates. The diffusion-controlled cure reaction was incorporated in the development of the kinetic model, and the model parameters were determined from isothermal experiments. The first order reaction was confirmed from the characteristic shape of isothermal cure thermograms, and the activation energy wes 78.43 kJ/mol. Finally, the proposed model was used to predict a complex autoclave thermal condition, which was composed of several isothermal and dynamic-heating stages.

• Korean Journal of Mathematics
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• v.4 no.1
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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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• 1994.10a
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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.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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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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• v.11 no.3
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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.

• Journal of the Korean Electrochemical Society
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• v.15 no.3
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• pp.165-171
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• 2012

Here is implemented MATLAB program to analyze the characteristic curves of cyclic voltammetry which involves the multi-electron electrode reaction considered as key processes in electrochemical systems. For the electrochemical mass-transfer system, Fick's concentration equation subject to semi-infinite diffusion model for the boundary condition was discretized and solved by the explicit finite difference method. The resulting concentration values were converted into currents at each node by using Butler-Volmer equation. Based on the good agreement between the present numerical solution and the existing experimental results, effects of kinetic constants and CV scan rates on the reaction mechanism in multi-electron transfer processes were investigated effectively.

• Nuclear Engineering and Technology
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• v.50 no.6
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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.