• Journal of the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.99-105
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• 1994

In this study, the transverse and the torsional vibration analyses of a precision dynamic drive system with the magnetic coupling are accomplished. The force of the magnetic coupling is regarded as an equivalent transverse stiffness, which has a nonlinearity as a function of the gap and the eccentricity between a driver and a follower. Such an equivalent stiffness is calculated by and determined by the physical law and the calculated equivalent stiffness is modelled as the truss element. The form of the torque function transmitted through the magnetic coupling is a sinusoidal and such an equivalent angular stiffness, which represents the torque between a driver and a follower, is modelled as a nonlinear spring. The main spindle connected to a follower is assumed to a rigid body. And then finally we have the nonlinear partial differential equation with respect to the angular displacements. Through the procedure mentioned above, we accomplish the results of the torsional vibration analysis in a spindle system with the magnetic coupling.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.291-307
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• 1996

In this paper, we shall show the existence of solutions of the following nonlinear partial differential equation $$ {^{divA(-\Delta u) = f(x, u, \Delta u) in \Omega}^{u = 0 on \partial\Omega} $$ where $f(x, u, \Delta u) = -u$\mid$\Delta u$\mid$^{p-2} + h, p \geq 2, h \in L^\infty$.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.119-130
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• 2002

An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.559-569
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• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.207-214
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• 2011

The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.947-951
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• 1989

A Class of nonlinear distributed parameter control problems is first stated in a partial differential equation form in multi-index notion and then converted into an integral equation form. Necessary conditions for optimality in the form of maximum principle are then derived in Sobolev space W$^{l}$, p/(1 leq. p .leq. .inf.)..

• Honam Mathematical Journal
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• v.31 no.1
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• pp.109-124
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• 2009

Based on the observed data for Clarithromycin released, three commonly used inflow models: the power, the exponential, and the logarithmic models are considered. Among them, the power model is used most in practice for simplicity. Using the numerical parameter estimation techniques, the parameters appeared in the model equations are estimated. Through the numerical estimation results using the several experimental data sets, the exponential model turns out to be best among the three models. More specifically, the sum of squares of absolute errors and the sum of squares of relative errors for the exponential model are reduced by 80-95 % for the experimental data sets and 60-90 % for the noise added data sets compared with those for the power and logarithmic models. A typical experimental data set is used in this paper to show the estimation method and its numerical results. The proposed numerical method and its algorithm are designed for estimating the parameters appeared in the model differential equations for which the exact form of the solution is unknown in general. The methodology developed can be applied to more general cases such as the nonlinear ordinary differential equations or the partial differential equations.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.491-505
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• 2010

A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton's principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).