• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.893-906
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• 2023

In this article, we are devoted to study the problem of the existence, uniqueness and positivity of the global solutions of the 3 × 3 reaction-diffusion systems with the total mass of the components with time. We also suppose that the nonlinear reaction term has a critical growth with respect to the gradient. The technique that we used to prove the global existence is the method of the compact semigroup.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.1-20
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• 2006

This paper presents the interior penalty discontinuous Galerkin finite element methods (DGFEM) for solving the rotating disk electrode problems in electrochemistry. We present results for the simple E reaction mechanism (convection-diffusion equations), the EC' reaction mechanism (reaction-convection-diffusion equation) and the ECE and $EC_2E$ reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively). All problems will be in one dimension.

• Nuclear Engineering and Technology
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• 제49권5호
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• pp.1019-1030
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• 2017

Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN_1 ${\rightarrow}$ RN_2 ${\rightarrow}$ RN_3) and a parallel reaction (RN_1 ${\rightarrow}$ RN_2A + RN_2B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.

• 대한수학회지
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• 제44권4호
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• pp.779-786
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• 2007

In this note, we consider a system of two reaction-diffusion equations with absorption, under homogeneous Dirichlet boundary. Using scaling methods, we establish the blow-up rate estimates.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.1015-1019
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• 2012

The direct calculation method is generalized to the excited-state diffusion-influenced reversible reaction of a neutral and a charged particle under an external field with two different lifetimes and quenching in three dimensions. The present method provides an alternative way to calculate the binding probability density functions and the survival probabilities from the corresponding irreversible results. The solutions are obtained as the series solutions by the diagonal approximation due to the anisotropy of the unidirectional external field. The numerical results are found to be in good agreement with those of the previous study [S. Y. Reigh et al. J. Chem. Phys. 132, 164112 (2010)] within a weak field limit. The solutions of two approaches show qualitatively the same overall behavior including the power laws at long times.

• Bulletin of the Korean Chemical Society
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• 제34권5호
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• pp.1454-1456
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• 2013

The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

• 대한수학회지
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• 제54권6호
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• 한국주조공학회지
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• 제26권1호
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• pp.27-33
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• 2006

Phase evolutions involving nucleation stages together with diffusional growth have been examined in order to provide a guideline for determining rate limiting stages during phase evolutions. In multiphase materials systems in coatings, composites or multilayered structures, diffusion treatments often result in the development of metastable/intermediate phases at the reaction interfaces. The development of metastable phases during solid state interdiffusion demonstrates that the nucleation reaction can be one controlling factor. Also, the concentration gradient and the relative magnitudes of the component diffusivities provide a basis for a phase selection and the application of a kinetic bias strategy in the phase selection. For multicomponent alloy systems, the identification of the operative diffusion pathway is central to control phase formation. Experimental access to the nucleation and growth stage is discussed in thin film multi layers and bulk samples.

• 호남수학학술지
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• 제30권3호
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• pp.411-423
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• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).