• Journal of applied mathematics & informatics
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• v.28 no.1_2
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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.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.693-707
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• 1996

Consider a specific class of scalar-valued reaction diffusion equations of the form $$ (1.1) u_t = \nu\Delta u + f(u), u \in R $$ where $\nu$ < 0 is viscosity parameter and $f : R \to R$ is sufficiently smooth.

• Applied Microscopy
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• v.45 no.1
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• pp.16-22
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• 2015

The reaction kinetics of the growth of Ni germanide in the Ni/Zr-interlayer/Ge system was investigated using isothermal in situ annealing at three different temperatures in a transmission electron microscope. The growth rate of Ni germanide in the Ni/Zr-interlayer/Ge system was determined to be diffusion controlled and depended on the square root of the time, with the activation energy of $1.04P{\pm}0.04eV$. For the Ni/Zr-interlayer/Ge system, no intermediate or intermixing layer between the Zr-interlayer and Ge substrate was formed, and thus the Ni germanide was formed and grew uniformly due to Ni diffusion through the diffusion path created in the amorphous Zr-interlayer during the annealing process in the absence of any intermetallic compounds. The reaction kinetics in the Ni/Zr-interlayer/Ge system was affected only by the Zr-interlayer.

• Journal of the Korean Electrochemical Society
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• v.8 no.2
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• pp.106-114
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• 2005

This article covers the theoretical ac-impedance models for the analysis of oxygen reduction on the porous cathode electrode f3r solid oxide fuel cell (SOFC). Firstly, ac-impedance models were explained on the basis of the mechanism of oxygen reduction, which were classified into the rate-determining steps; (i) adsorption of oxygen atom on the electrode surface, (ii) diffusion of adsorbed oxygen atom along the electrode surface towards the three-phase (electrode/electrolyte/gas) boundaries, (iii) surface diffusion of adsorbed oxygen atom m ixed with the adsorption reaction of oxygen atom on the electrode surface and (iv) diffusion of oxygen vacancy through the electrode coupled with the charge transfer reaction at the electrode/gas interface. In each section for ac-impedance model, the representative impedance plots and the interpretation of important parameters attributed to the oxygen reduction reaction were explained. Finally, we discussed in detail the applications of the proposed theoretical ac-impedance models to the real electrode of SOFC system.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1255-1262
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• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.