• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.735-769
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• 2019

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.6
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• pp.1149-1157
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• 1994

In this case of the mobile communication of vehicles with satellite, the signal at attenuation is due to roadside trees. To analyze this signal attenuation, a roadside tree was modeled as different obstacles of rectangular type and then using Fresnel and Kirchhoff diffraction theory, a formula was derived for signal intensity variation caused by the roadside tree model. The signal attenuation of a roadside tree model was obtained by numerical analysis with variation of the elevation angle, the position and distance between a receiver and a transmitter, and these were compared with experimental results. The results of comparison between theoretical and experimental values show, as expected, the good agreement of the signal attenuation trend.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1988.10a
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• pp.126-130
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• 1988

In this paper the intensity variation of electromagnedtic wave is computed with Huygens Fresnel’s theory using diffraction plaenomethon. An obstacle or an aperture with pertangular type between a transmitter and a receiver is consider and the frequency is selcetde in a car phone system band(870~1500MHz) For numerical analysis Fresnel integral equation is developed which is based on the Kirchhoff’s diffraction theory. The result with the obstacle’s dimension from finite value to extremely large confirms the validity of computer simulation.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.145-153
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• 1991

A numerical simulation of the nonsteady state rolling process in the plane strain condition is presented in the basis of the rigid-plastic finite element method by considering large deformation. In order to apply the large deformation theory to the numerical method for sheet rolling problems, constitutive equation relating 2nd-Piola Kirchhoff stress and Lagrangian strain which reflect geometrical nonlinearity is used. To confirm the validity of the developed algorithm, the analysis of the neutral flow region, roll separating force, torque, pressure and stress/strain distributions on the workpiece is conducted from the bite of the material until the steady state is reached. The computed results of the roll force and torque in the present finite element analysis are lower than those corresponding to small strain theory. The pressure distribution at the work piece-roll interface is found to show the typical 'friction hill' type only. The peak value in near the neutral region, however, is good agrements with the existing results. the neutral region, however, is good agrements with the existing results. The frictional force at the roll interface provide detailed information about the neutral point where the shear forces change direction. In addition, the analysis also includes the effect and influence of material condition, strip thickness, work roll diameter, as well as roll speed and lubricant on each deformation process.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.43-50
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• 2000

In the first-order shear deformation laminated beam theory (FSDT), the Kirchhoff hypothesis is relaxed such that the transverse normals do not remain perpendicular to the midsurface after deformation. Bending behavior of laminated composite thin-walled beams with singly- and doubly-symmetric open sections under uniformly distributed and concentrated loads is analyzed by the Timoshenko-type thin-walled beam theory. A closed-form expression for the shear correction factor of I-shaped composite laminated section is obtained. Numerical examples are presented to compare present analytical solutions by FSDT with the finite element solutions obtained by using three dimensional model. The effects of lamination of scheme and length-to-height ratio on the shear deformation of laminated composite beams with various boundary conditions are studied.

• Smart Structures and Systems
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• v.17 no.2
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• pp.257-274
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• 2016

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.6
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• pp.1221-1226
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• 2011

In order to analyze the receiver gain characteristic of the Soret-type FZPL lens antenna which is operated at 12GHz, TLM method can be applied. The application of the FZPL lens antenna is often use the receiver for satellite TV system, radio telescope, and Geodetic System. Some numerical results computed by TLM method are compared with Kirchhoff's approximation and PO method. The focal characteristic of receiver gain on main axis of the FZPL is mostly shown at the front side, which means that the position of the receiver should be properly calibrated.