• 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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.443-459
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• 2006

The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\;{\leq}\;{\infty}$. By obtaining the bounds of $W\array_2^1$-norms of the local solution independent of T we establish the global existence of the solution. And the long-time behaviors of the global solution are analyzed when the diffusion rates $d_1\;and\;d_2$ are sufficiently large.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.47-51
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• 2001

We establish the global existence of nonnegative solutions to some reaction-diffusion equation for exponential nonlinearity for small initial data.

• Journal of Information Technology Services
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• v.11 no.1
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• pp.305-323
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• 2012

This study examines online social media diffusion across different countries that will help to provide a picture of current global online social network services (SNSs). Analyzing country-level data drawn from 78 nations, we find that non-technological factors such as culture and language as well as technological factors including Internet penetration rate and smartphone adoption rate have significant effects on online social media diffusion. These findings, derived from a broad range of different countries, not only provide theoretical insights into understanding critical factors that enable successful global expansion of online social media services but also help practitioners plan their marketing strategies more effectively in a global context.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• Journal of applied mathematics & informatics
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• v.41 no.4
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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.

• Transactions on Electrical and Electronic Materials
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• v.13 no.6
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• pp.273-277
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• 2012

The vacuum drying process for drying of paper in current transformers was modeled with an aim to develop an understanding of the drying mechanism involved and also to predict the water collection rates. A molecular as well as macroscopic approach was adopted for the prediction of drying rate. Ficks law of diffusion was adopted for the prediction of drying rates at macroscopic levels. A steady state and dynamic mass transfer simulation was performed. The bulk diffusion coefficient was calculated using weight loss experiments. The accuracy of the solution was a strong function of the relation developed to determine the equilibrium moisture content. The actually observed diffusion constant was also important to predict the plant water removal rate. Thermo gravimetric studies helped in calculating the diffusion constant. In addition, simulation studies revealed the formation of perpetual moisture traps (loops) inside the CT. These loops can only be broken by changing the temperature or pressure of the system. The change in temperature or pressure changes the kinetic or potential energy of the effusing vapor resulting in breaking of the loop. The cycle was developed based on this mechanism. Additionally, simulation studies also revealed that the actual mechanism of moisture diffusion in CT's is by surface jumps initiated by surface diffusion balanced against the surrounding pressure. Every subsequent step in the cycle was to break such loops. The effect of change in drying time on the electrical properties of the insulation was also assessed. The measurement of capacitance at the rated voltage and one third of the rated voltage demonstrated that the capacitance change is within the acceptance limit. Hence, the new cycle does not affect the electrical performance of the CT.

• Journal of the Korean Society of Safety
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• v.26 no.1
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• pp.21-26
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• 2011

Extinction and ignition characteristics of $CH_4$-air counterflow diffusion flame were numerically investigated using a Flame-Controlling Method(FCM). A skeletal reaction mechanism, which adopts 17 species and 58 reactions, was used in the simulation. The extinction and ignition conditions of the $CH_4$-air diffusion flames were investigated with varying the global strain rate. Upper and middle branches of S-curve for the peak temperature in the inverse of the global strain rate space were obtained with the FCM. The structures of diffusion flames in the upper and middle branches of S-curve were compared. It was found that the global strain rate was not correlated with the local strain rate well in the low global strain rate region. It is expected that the FCM is very useful to obtaining the extinction and ignition condition of diffusion flame, such as fires.

• Journal of Contemporary Eastern Asia
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• v.14 no.1
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• pp.45-55
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• 2015

This paper examines the diffusion of smartphones with a special emphasis on the diffusive interactions between Apple iOS and Google Android in a global context. Since the two mobile platforms were first introduced in the market, the use of smartphones has skyrocketed, suggesting that the dramatic diffusion of smartphones may be explained in part by the growth and competition of these two platforms. To study this, an extended Bass model is applied to a data set of quarterly smartphone sales between 2008 and 2013 for 15 countries. Our findings suggest that the innovation effect was more salient for iOS than for Android in developed countries, whereas the imitation effect was more striking for Android than for iOS in developing countries. Furthermore, our results from the co-diffusion model suggest that the diffusion of Android negatively affected by the diffusion of iOS, but not vice versa.