• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-699
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• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.285-297
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• 2013

This paper deals with parabolic equations coupled via nonstandard growth sources, subject to homogeneous Dirichlet boundary conditions. Three kinds of necessary and sufficient conditions are obtained, which determine the complete classifications for non-simultaneous and simultaneous blowup phenomena. Moreover, blowup rates are given.

• Korean Journal of Food Science and Technology
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• v.28 no.1
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• pp.122-126
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• 1996

Growth patterns of Saccharomyces cerevisiae NS 2031 and its total RNA contents were observed by a fed-batch fermentation with different media-feeding methods. With an exponential feeding pattern, both final cell concentrations and intracellular RNA contents decreased with increasing feeding rates. Intracellular RNA contents also decreased with the growth time. At the same feeding rate of the exponential pattern, final cell concentrations decreased with the increase of total sugar concentration whereas intracellular RNA contents increased. The highest cellular yield was 0.47 at the total sugar concentration of 10%. With increasing feeding rates of the parabolic feeding pattern, final cell concentrations decreased whereas intracellular RNA contents increased, showing a different tendency from the exponential feeding pattern. In comparison of two feeding methods, the exponential feeding pattern was better than the parabolic feeding pattern in terms of cell growth, cellular yields and intracellular RNA contents of Saccharomyces cerevisiae NS 2031. Also, the intracellular RNA contents of the exponential feeding pattern was found to be about 2% higher than that of the parabolic feeding pattern at the same instantaneous growth rate $({\mu}_{inst})$.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.151-167
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• 1997

We estimate the interior Lipschitz norm and maximum of the solution for degenerate parabolic equations with absorption. Also obtain the growth rate of the solution $u$ in terms of time $t$. From this we show the uniqueness of solution with respect to the initial trace.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.145-161
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• 2020

In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.

• Journal of the Korean Ceramic Society
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• v.25 no.4
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• pp.329-334
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• 1988

Kinetics of grain growth in PLZT ceramics during isothermal heat treatment and hot-pressing were investigated and the published data on grain growth were reanalyzed. It was found, in many cases, that the errors were introduced by ignoring the initial grain size. The grain growth of PLZT ceramics was confirmed to follow the parabolic normal growth : D2-Do2=Kt.

• Journal of the Korean Society for Heat Treatment
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• v.14 no.5
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• pp.282-285
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• 2001

Based on the mass balance of anion and cation fluxes, the parabolic rate constant ($K_p$) of oxide grown during the high-temperature oxidation of metal is theoretically calculated. It is assumed that the diffusion of oxygen anion and metal cation through oxide scale obeys the Fick's 1st law, the growth of oxide is controlled by the diffusion of ions, electrical potential gradient as driving force for diffusion of ions is ignored, and oxidation occurs within an existing oxide layer. Then, the parabolic rate constant can be expressed by $K_p=[2{\rho}_{MmOn}{M^2}_{MmOn}(mD_oC_o{^e}+nD_MC_M{^e})/nm]$.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.531-551
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• 2018

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

• Journal of the Korean Ceramic Society
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• v.33 no.1
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• pp.25-34
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• 1996

Yttria stabilized zirconia (YSZ) thin films were prepared by the electrochemical vapor deposition (EVD) method on the porous Al2O3 substrates which were fabricated by different substrate thickness and porosity. Film growth rates decreased with increase on the substrate thickness and porosity and obeyed a parabolic rate law. Activa-tion energy calculated from the parabolic rate onstants was 69.9 kcal/mol. With increase on the deposition time, monoclinic phase was appeared and then disappeared. YSZ penetrated deeply into substrates when the EVD temperature decreased. Electrical conductivity of the films was 0.09 S/cm at 100$0^{\circ}C$ similar to the value of YSZ single crystal.

• Journal of the Korean Ceramic Society
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• v.32 no.3
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• pp.371-377
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• 1995

Silicon oxide films were grown on single-crystal silicon substrates at low temperatures (25~205$^{\circ}C$) in a low pressure electron cyclotron resonance (ECR) oxygen plasma. The growth rate of the silicon oxide film increased as the temperature increased or the pressure decreased. Also, the thickness of the silicon oxide film increased at negative bias voltage, but not changed at positive bias voltage. The growth law of the silicon oxide film was approximated to the parabolic form. Capacitance-voltage (C-V) and current density-electric field (J-E) characteristics were studied using Al/SiO2/p-Si MOS structures. For a 10.2 nm thick silicon oxide film, the leakage current density at the electric field of 1 MVcm-1 was less than 1.0$\times$10-8Acm-2 and the breakdown field was higher than 10 MVcm-1. The flat band voltage of Al/SiO2/p-Si MOS capacitor was varied in the range of -2~-3 V and the effective dielectric constant was 3.85. These results indicate that high quality oxide films with properties that are similar to those of thermal oxide film can be fastly grown at low temperature using the ECR oxygen plasma.