• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.247-262
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1811-1816
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• 1991

In this paper we present how the deviation bound, which is a synchronic variable, can be used for checking liveness in Petri nets. Also, the deviation bound will be applied to detect or avoid deadlock situations and to characterize concurrency against sequential behaviors in automated manufacturing systems. In the current stage, we restrict the applicable domain of these methods to the Petri net structure that can be synthesized by combining common transitions or common places or common paths of Live-and-Bounded circuits.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• Journal of the Korea Computer Industry Society
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• v.3 no.5
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• pp.569-574
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• 2002

We model the torsional oscillation of a suspension bridge, which is the forced sine-Cordon equation on a bounded domain. We use finite difference method to solve nonlinear partial differential equation numerically. The partial differential equation has multiple periodic solutions. Whether the span oscillates with small or large amplitude depends oかy on its initial displacement and velocity. Moreover, we observe that the qualitative properties are consistent with the behavior observed at the Tacoma Narrows Bridge on the day of its collapse.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.855-860
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• 2006

In this paper, a numerical case study is carried out on the hydroelastic vibration of rectangular plate with various fluid field. It is assumed that the tank wall is clamped along the plate edges. The VMM(Virtual Mass Method) of Nastran is used for the simulation of fluid domain and calculating natural frequency of fluid-coupled structure. In this paper, natural frequencies are calculated and compared for rectangular plates with various fluid field such as infinite fluid and finite fluid, length change of finite fluid field and various fluid contacting conditions.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.217-231
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• 2010

We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.127-139
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• 2000

Transient aerodynamic response of an airfoil to a rapidly deploying spoiler is numerically investigated using a two-dimensional turbulent compressible Navier-Stokes flow model. The spoiler moving relative to a stationary airfoil is treated by an overset grid bounded by a 'dynamic domain-dividing line' the concept of which is developed first..in this paper. The fluid-dynamic mechanism of the adverse lift due to the rapidly deploying spoiler is analyzed. Also the effect of spoiler deploying rate on the initial behavior of the aerodynamic response is expounded, which is of interest in view of active control technology and controller design for the spoiler. The results of present computation about the stationary as well as moving spoilers are relatively in good agreement with the existing experimental data.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.737-748
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• 2012

The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $$-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}$$ with Dirichlet boundary condition in a bounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, where $h(x){\in}L^1_{loc}({\Omega})$, $f(x,s)$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $H^1_0({\Omega})$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.409-421
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• 2014

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: $$\{-div\((1+\frac{|{\nabla}u|^{p(x)}}{\sqrt{1+|{\nabla}u|^{2p(x)}}}})|{\nabla}u|^{p(x)-2}{\nabla}u\)={\lambda}f(x,u)\;a.e.\;in\;{\Omega}\\u=0,\;on\;{\partial}{\Omega}$$ where ${\Omega}{\subset}R^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\lambda}$ > 0 is a parameter. The purpose of this paper is to obtain the existence results of nontrivial solutions for every parameter ${\lambda}$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter ${\lambda}$ > 0. Then we consider the continuation of the solutions. Our results are a generalization of that of Manuela Rodrigues.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1471-1484
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• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.