• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.53-64
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• 2007

In this paper, we apply the generalized quasilinearization technique to a forced Duffing equation with three-point mixed nonlinear nonlocal boundary conditions and obtain sequences of upper and lower solutions converging monotonically and quadratically to the unique solution of the problem.

• Journal of the Chungcheong Mathematical Society
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• v.2 no.1
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• pp.9-14
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• 1989

Certain type of singular two point boundary value problem is studied. This contains a wider class of differential equations than [5]. An example is provided for comparison with earlier results.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.877-882
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• 2010

In this paper, a third-order three-point boundary value problem on time scales is considered. We establish criteria for the existence of a solution and a positive solution by using the Leray-Schauder fixed point theorem. An example is also given to illustrate our results.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.267-277
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• 2011

This paper is concerned with eigenvalues of second-order vector equations on time scales with boundary value conditions. Properties of eigenvalues and matrix-valued solutions are studied. Relationships between eigenvalues of different boundary value problems are discussed.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.237-250
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• 1995

A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.457-470
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• 2008

This paper is concerned with the robust boundary control of the chemotaxis reaction diffusion system. That is, we show that the existence of the saddle point for the robust control problem when the control and the disturbance are given by the boundary condition.

• East Asian mathematical journal
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• v.29 no.5
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• pp.491-501
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• 2013

This paper is concerned with the necessary conditions of the optimal boundary control for some chemotaxis equations. We obtain the existence and the necessary conditions of the optimal boundary control in the space $(H^1(0,T))^2$. Moreover, under some assumptions, we show the uniqueness of the optimal control.

• Journal of Families and Better Life
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• v.9 no.2
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• pp.345-366
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• 1991

The concrete purpose of this study is to examine the possibility of applying S.Minuchin's structural family therapy theory to each clinical families so that it can solve efficiently the clinical problems Korean family. The test results are as follows: 1)The Results of Question I : Types of Korean family problems can be divide into six. Then the most frequent type of problem was marital problem. 2) The Results of Question II: Korean normal family showed rater difussed boundary and higher rate of wife dominant type than that of husband dominant type in aspect of boundary and power, and had low tendency toward alignment and neutral adjustment. 3)The Results of Quesion III; Amidst the clinical families, family structural traits of the families which have marital problems showed a clear boundary, the tendency toward alignment, and higher tate of husband dominant type than that of wife dominant type. And family structural traits of children problem family had the tendency of alignment and showed little wife-dominanted families in power. Finally, mother-in -law and daughter-in-law problemed family had several characters such as diffused boundary, the tendency of alignment and high adjustment. 4)The Results of Question IV : As a result of camparing problemed families with normal families in family structure, there was high adaptability of S.Minuchin's structural theory to the two family groups; the groups of marital problems and those of children problem.

• Earthquakes and Structures
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• v.9 no.1
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• pp.173-194
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• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.355-362
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in various problems. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem and fillet problem are chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in these problems.