• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.11
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• pp.898-906
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• 2014

This paper presents a reduction method for a straight-line path error of a flexible beam deploying from a rotating rigid hub. Previous studies discussed about only vibration phenomena of flexible beams deploying from rotating hubs; however, this study investigates a vibration reduction of a rotating beam with variable length. The equation of motion and associated boundary conditions are derived for a flexible beam deploying from a rotating rigid hub, and then they are transformed to a variational equation. By applying the Galerkin method, the discretized equations are obtained from the variational equation. Based on the discretized equations, the dynamic responses of a rotating/deploying beam are analyzed when the beam end has a straight line motion. A reduction method for the trajectory error is proposed, using the average length of a rotating/deploying beam. It is shown that the proposed method is able to reduce the residual vibration of a rotating/deploying beam.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.37-49
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• 2000

This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1091-1101
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• 2018

We concern in this paper the graph Kazdan-Warner equation $${\Delta}f=g-he^f$$ on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h{\leq}0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

• Journal of Ocean Engineering and Technology
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• v.15 no.2
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• pp.6-10
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• 2001

Water waves propagate over irregular bottom bathymetry are transformed by refraction, diffraction, shoaling, reflection etc. Principal factor of wave transform is bottom bathymetry, but in case of current field, current is another important factor which effect wave transformation. The governing equation of this study is develope as wave-current equation type to investigate the effect of wave-current interaction. It starts from Berkhoff's(1972) mild slope equation and is transformed to time-dependent hyperbolic type equation by using variational principal. Finally the governing equation is shown as a parabolic type equation by splitting method. This wave-current model was applied to the kwangan beach which is located at Pusan. The numerical simulation results of this model show the characteristics of wave transformation and flow pattern around the Kwangan beach fairly well.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.133-147
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• 2024

Let G = (V, E) be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on G $${\Delta}u={\lambda}e^u(e^u-1)^5+4{\pi}\sum_{s=1}^{N}\delta_{ps}$$, where λ > 0, δ_ps is the Dirac mass at the vertex p_s, and p₁, p₂, . . . , p_N are arbitrarily chosen distinct vertices on the graph. We show that there exists a critical value $\hat{\lambda}$ such that when λ > $\hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when λ = $\hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when λ < $\hat{\lambda}$, the generalized Chern-Simons equation has no solution.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.203-217
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• 1994

In this paper we develop an exponentialization procedure for the modelling of open FMS networks with general processing time at each station and limited buffer size. By imposing a reasonable assumption on the solution set, the nonlinear equation system for the exponentialization procedure is formulated as a variational inequality problem and the solution existence is examined. The efficient algorithm for the nonlinear equation system is developed using linearized Jacobi approximation method.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.867-885
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• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.