• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1457-1470
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• 2017

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.

• East Asian mathematical journal
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• v.22 no.2
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• pp.171-188
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• 2006

We consider the problem of an optimal control of the wave equation with a localized nonlinear dissipation. An optimal control is used to bring the state solutions close to a desired profile under a quadratic cost of control. We establish the existence of solutions of the underlying initial boundary value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1431-1437
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• 2010

We use the (G'/G)-expansion method to seek the traveling wave solution of the Seventh-order Sawada-Kotera Equation. The solutions that we get are more general than the solutions given in literature. It is shown that the (G'/G)-expansion method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.509-518
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• 2001

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1013-1024
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• 2007

In this paper we consider the uniform decay for the wave equation of Carrier model subject to memory condition at the boundary. We prove that if the kernel of the memory decays exponentially or polynomially, then the solutions for the problems have same decay rates.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.205-216
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• 2022

This paper deals with a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. This work is devoted to prove a global nonexistence of solutions for a nonlinear wave equation with nonnegative initial energy as well as negative initial energy.

• Journal of the Society of Naval Architects of Korea
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• v.60 no.5
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• pp.341-350
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• 2023

In this paper, numerical experiments are performed to examine the collision between a solitary wave and a wave-packet (dispersive wave) in shallow water. We attempt to introduce the improved Boussinesq equation governing the experiments, which is solved by using a semi-analytical approach, called Pseudo-parameter Iteration method(PIM). Using various numerical experiments, we have observed that the wave-packet (propagating dispersive wave) experiences a phase shift after collision with a solitary wave. This phenomenon may be considered as a nonlinear wave-wave interaction in shallow water.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.22-30
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• 1989

Wave propagation is changed by the effect of shoaling, current-depth refraction and shelter-ing etc. To solve these problems. numerous models have been developed. In the present study, a coordinate system is proposed based on the wave ray equation with the wave number equation including diffraction effects . The governing equation for the study was derived from the mild slope wave equation in non-steady state, including current effects (Kirby, 1986a) and trans-formed into an orthogonal curvilinear coordinate system on the basis of the wave ray equation. To obtain a numerical solution, an explicit finite difference scheme was used, and solved by the relaxation method. This model was tested for various cases: Firstly a submersed circular shoal and a constant unit depth. Secondly a submerged elliptic shoal on a slope, and finally a breakwater harbour with obliquely incident waves on a slope. The model was found to simulate the experimental results and other theoretical results in wave height and wave angle fairy well, and the applicability of the model around an arbitrary shaped coastal structure was also verified. To demonstrate the general usefullness of the present approach , the model is to be applied to a field situation with a complex bed topography.

• Journal of Ocean Engineering and Technology
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• v.15 no.4
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• pp.14-19
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• 2001

In this paper, the wave and current forces acting on cylinders are investigated by theoretical and experimental methods. The models used are one-cylinder, four-cylinder and semi-submersible types. The theoretical investigations are carried out by the Morison equation and three dimensional source distribution method to calculate exciting forces in waves with and without currents. The experimental investigations are carried out in the wave tank which can generate currents in both directions. In these tests, the models have been exposed to the regular waves with and without currents. It is shown that the exciting forces acting on the one-cylinder or four-cylinders can be approximately estimated by the Morison equation and also by the diffraction theory. However, the Morison equation seems to be not appropriate to estimate the exciting forces on the present type of semi-submersible.