• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• Korea-Australia Rheology Journal
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• v.13 no.3
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• pp.141-148
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• 2001

In this research, experimental studies leave been performed on the hydrodynamic interaction between a spherical particle and a plane wall by measuring the force between the particle and wall. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1,000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia plays all important role in the particle-wall interaction in Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in Newtonian fluid. In non-Newtonian fluid, normal stress difference and viscoelasticity play important roles as expected. In the dilute solution weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also affect the physic of the problem.

• Smart Structures and Systems
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• v.23 no.6
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• pp.521-536
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• 2019

Using magnetorheological (MR) dampers in multiswitch open-loop control mode has been shown to be cost-effective for cable vibration mitigation. In this paper, a method for analyzing the damping performance of taut cables incorporating MR dampers in open-loop control mode is developed considering the effects of damping coefficient, damper stiffness, damper mass, and stiffness of the damper support. Making use of a three-element model of MR dampers and complex modal analysis, both numerical and asymptotic solutions are obtained. An analytical expression is obtained from the asymptotic solution to evaluate the equivalent damping ratio of the cable-damper system in the open-loop control mode. The individual and combined effects of the damping coefficient, damper stiffness, damper mass and stiffness of damper support on vibration control effectiveness are investigated in detail. The main thrust of the present study is to derive a general formula explicitly relating the normalized system damping ratio and the normalized damper parameters in consideration of all concerned effects, which can be easily used for the design of MR dampers to achieve optimal open-loop vibration control of taut cables.

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.5
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• pp.35-45
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• 1981

An asymptotic solution of electromagnetic waves scattered by a right-angled dielectric wedge for plane wave incidence is obtained. Scattered fields are constructed by waves reflected and refracted from dielectric interfaces (geometric-optical fields) and a cylindrical wave diffracted from the edge. The edge diffracted field is obtained by adding a correction to the edge diffraction of physical optics approximation, where the correction field is calculated by solving a dual series equation amenable to simple numerical calculation. Validity of this result is assured by two limits of relative dielectric constant $\varepsilon$ of the wedge. The total asymptotic field calculated results in a Rawlins' Neumann series solution for small $\varepsilon$, and the edge diffraction pattern is shown to approach that of a perfectly conducting wedge for large $\varepsilon$. Calculated field patterns are presented and the accuracy of physical optics approximation is discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1245-1252
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• 1994

A solution of heat transfer problems of composite materials has been tried using homogenization technique. Homogenization technique, which was derived by applying asymptotic expansion to the standard finite element method, helped compute the equivalent thermal conductivity matrices of base cells which constituted the composite material with repeated patterns. The homogenization technique made it possible to compute the solution of the heat transfer problem of composite materials with lower degrees of freedom compared to those of other numerical methods. The equivalent thermal conductivities computed by computed by homogenization technique are also applicable to other numerical methods such as finite difference method.

• Nuclear Engineering and Technology
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• v.41 no.3
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• pp.279-286
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• 2009

Improving over a previous study [1], this paper provides a Monte Carlo method for the heat conduction analysis of problems with complicated geometry (such as a pebble with dispersed fuel particles). The method is based on the theoretical results of asymptotic analysis of neutron transport equation. The improved method uses an appropriate boundary layer correction (with extrapolation thickness) and a scaling factor, rendering the problem more diffusive and thus obtaining a heat conduction solution. Monte Carlo results are obtained for the randomly distributed fuel particles of a pebble, providing realistic temperature distributions (showing the kernel and graphite-matrix temperatures distinctly). The volumetric analytic solution commonly used in the literature is shown to predict lower temperatures than those of the Monte Carlo results provided in this paper.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.227-241
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• 2016

A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.