• 한국연소학회지
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• 제7권1호
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• pp.8-14
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• 2002

Measurements of global emissions, flame radiation and flame dimensions are presented for unconfined turbulent-jet and precessing-jet diffusion flames. Precessing jet flames are characterised by increases in global flame radiation and global flame residence time for methane and propane fuels, however a strong dependency of the NOx emission indices on the fuel type exists. The fuel type dependence is considered to be because soot radiation is more effective than gas-radiation at reducing global flame temperatures relative to adiabatic flame temperatures and reducing the NO production rate.

• 대한수학회보
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• 제35권4호
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• 대한수학회지
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• 제57권1호
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Journal of Electrochemical Science and Technology
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• 제2권3호
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• pp.174-179
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• 2011

The mesoscopic $Sb_2S_3$-sensitized photoelectrochemical solar cells using cobalt redox electrolyte exhibit nonlinear behavior of power conversion efficiency with illuminated sun intensity. From the measurement of bulk diffusion and electrochemical impedance spectroscopy studies, we suggest that the nonlinearity of device performance with illuminated sun intensity is attributed not to the slow bulk diffusion problem of cobalt electrolyte but to the limited mass transport in narrowed pore volume in mesoscopic $TiO_2$ electrode.

• IEIE Transactions on Smart Processing and Computing
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• 제6권2호
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• pp.124-128
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• 2017

A light guide improves the spatial resolution of a gamma ray imaging system by diffusing the scintillation light. Similarly, light diffusion film, which has been applied to flat-panel-display engineering, spreads the light from the light guide panel. In this study, we adopted light diffusion film for the light guide of a gamma ray imaging system, and evaluated its diffusion characteristics. We compared the light diffusion performance of the film to an ordinary acrylic plate. As a result, the diffusion film widely spreads scintillation light. As for the thickness of the light guide, we acquired more distinct images with three films overlapped than with an acrylic plate. We expect light diffusion film to be a promising candidate for light guides in gamma ray imaging systems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.43-55
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• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• 대한수학회지
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• 제51권3호
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• pp.635-654
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• 2014

We consider the Cauchy problem for a Keller-Segel-fluid model with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.

• 대한수학회지
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• 제47권6호
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• pp.1317-1328
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• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• 대한수학회논문집
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• 제23권2호
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.547-554
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• 2014

In this paper, we consider the existence and uniqueness of global weak solution for a sixth-order classical surface-diffusion equation in one spatial dimension. Moreover, the regularity and blow-up of solutions are also studied.