• Honam Mathematical Journal
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• v.30 no.3
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• pp.469-478
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• 2008

This paper is concerned with the boundary control of the chemotaxis reaction diffusion system. That is, we show the existence of the solution for the chemotaxis system with the boundary control and the existence of the optimal boundary control.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.457-470
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• 2008

This paper is concerned with the robust boundary control of the chemotaxis reaction diffusion system. That is, we show that the existence of the saddle point for the robust control problem when the control and the disturbance are given by the boundary condition.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• Journal of the Earthquake Engineering Society of Korea
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• v.19 no.1
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• pp.37-43
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• 2015

This paper presents a detailed procedure for a nonlinear soil-structure interaction of a seismically isolated NPP(Nuclear Power Plant) structure using the boundary reaction method (BRM). The BRM offers a two-step method as follows: (1) the calculation of boundary reaction forces in the frequency domain on an interface of linear and nonlinear regions, (2) solving the wave radiation problem subjected to the boundary reaction forces in the time domain. For the purpose of calculating the boundary reaction forces at the base of the isolator, the KIESSI-3D program is employed in this study to solve soil-foundation interaction problem subjected to vertically incident seismic waves. Wave radiation analysis is also employed, in which the nonlinear structure and the linear soil region are modeled by finite elements and energy absorbing elements on the outer model boundary using a general purpose nonlinear FE program. In this study, the MIDAS/Civil program is employed for modeling the wave radiation problem. In order to absorb the outgoing elastic waves to the unbounded soil region, spring and viscous-damper elements are used at the outer FE boundary. The BRM technique utilizing KIESSI-3D and MIDAS/Civil programs is verified using a linear soil-structure analysis problem. Finally the method is applied to nonlinear seismic analysis of a base-isolated NPP structure. The results show that BRM can effectively be applied to nonlinear soil-structure interaction problems.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.659-676
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• 2006

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.23 no.6
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• pp.383-391
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• 2011

Numerical simulations have been conducted for the cylindrical steam reformer having various boundary temperature distributions. $CH_4$, $H_2O$, CO, $H_2$ and $CO_2$ are often generated or destroyed by the reactions, namely the Steam Reofrming(SR) reaction, the Water-Gas Shift (WGS) reaction and the Direct Steam Reforming(DSR) reaction. The SR and the DSR reactions are endothermic reactions, and the WGS reaction is an exothermic reaction. The rate of reactions can be slightly controlled by artificially given boundary temperature distributions. Therefore, the component ratio of the gases at the outlet are different for various boundary temperature distributions, namely the constant, cubic and linear distributions. Among these distributions, the linear temperature distribution is outstanding for efficient hydrogen production of the steam reformer.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Journal of the Korean Ceramic Society
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• v.33 no.6
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• pp.718-724
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• 1996

Deformation mechanism map of Langdon-Mohammed type for YBa2Cu3O7-x superconducting ceramic was constructed by considering mechanisms of Nabarro-Herring Coble and powder-law creep and grain boundary sliding (GBS) with an accommodation by grain boundary diffusion. The map was found consistent with experi-mental results not only of the creep the also of the superplastic deformation. It showed the transition from interface reaction-controlled to the grain boundary diffusion-controlled GBS mechanism at about 1 ${\mu}{\textrm}{m}$ grain size and 100 MPa flow stress in agreement with the experimental results.

• Journal of the Korean Society of Combustion
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• v.18 no.3
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• pp.31-37
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• 2013

Numerical simulations are conducted to investigate the feature of spontaneous ignition of hydrogen within a certain length of downstream tube released by the failure of pressure boundaries of various geometric assumption. The results show that the ignition feature can be varied with the shape of pressure boundary. The ignition at the contact region are developed at the spherical pressure boundaries due to multi-dimensional shock interactions, whereas the local ignition is developed in limited area such as boundary layer at the planar pressure boundary conditions. The spontaneous ignition inside the tube can be generated from the reaction region of only boundary layer regardless of existence of the reaction of core region.