• 대한수학회지
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• 제46권4호
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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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• 제31권1_2호
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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.

• 한국식품과학회지
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• 제28권1호
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• pp.122-126
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• 1996

Saccharomyces cerevisiae NS 2031의 유가식 배양에서 기질공급방법에 따라 효모 생육과 RNA 축적을 관찰하였다. Exponential feeding 형태에서 기질공급속도가 빠를 때 최종 배양 시간에서 균체량과 새포내 RNA 함량은 감소하는 경향을 나타내었으며, 배양시간이 경과함에 따라 균체내 RNA 함량은 전반적으로 감소하는 경향을 나타내었다. Exponential feeding 형태의 동일한 기질공급속도에서, 기질공급농도가 높을수록 최종 균체량은 감소하였으며, 균체수율(Yx/s)은 10%의 기질공급농도에서 0.47로 가장 높았다. 균체내 RNA 함량은 기질공급농도가 높을수록 증가하는 경향을 보였다. Parabolic feeding 형태에서는 기질공급속도가 빠를수록 균체량은 감소하였으나, 균체내 RNA 함량은 증가하여 exponential feeding 형태에서와 다른 경향을 나타내었다. 두가지 기질공급형태에서 균체생육에 가장 좋은 기질공급 program의 결과를 비교해 보면, 균체량, 균체수율, 세포내 RNA 함량을 높이려면 exponential feeding 형태가 parabolic feeding 형태보다 유리하였다. 또한, 유가식 배양에서 같은 instantaneous growth rate $({\mu}_{inst})$에서 균체내 RNA 함량을 비교하면, exponential feeding이 parabolic feeding보다 2%가량 높게 유지되어, 기질공급형태가 균체내 RNA 축적 생리에 큰 영향을 주고 있음을 알았다.

• Korean Journal of Mathematics
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• 제5권2호
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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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• 제60권1호
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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.

• 한국세라믹학회지
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• 제25권4호
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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.

• 열처리공학회지
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• 제14권5호
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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 $K_p=[2{\rho}_{MmOn}{M^2}_{MmOn}(mD_oC_o{^e}+nD_MC_M{^e})/nm]$.

• 대한수학회지
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• 제55권3호
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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.

• 한국세라믹학회지
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• 제33권1호
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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.

• 한국세라믹학회지
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• 제32권3호
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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.