• 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 ).

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.812-819
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. This research provides the time pattern of TS in time domain, which is applicable to pulse modulated acoustic pressure field. If the time pattern of TS is predicted by using TS equation in frequency domain, it takes long time and difficult since time function pulsed acoustic wave may be decomposed into their frequency domain components. But TS equation in time domain has a convenience. If the expression for pulsed acoustic field has been obtained, the problem can be solved. Furthermore this paper introduces about mathematical equivalence quantities between EM wave and Acoustic Wave.

• 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.