• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.4
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• pp.296-308
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• 2001

A fully nonlinear Boussinesq equation of Wei et al. is finite differenced by Adams predictor-corrector method. A spatially distributed source function and sponge layers are used to reduce the reflected waves in the domain and wale breaking mechanism is included in the equation. The generated waves are found to be good and the corresponding wale heights are very close to the target values. The shoaling of solitary wave and transformation of regular wave over submerged shelf were simulated successfully. The characteristics of breaking mechanism was identified through the numerical experiment and the results of two dimensional wave propagation test over the spherical shoal showed the importance of nonlinear wave model.

• Journal of KSNVE
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• v.9 no.6
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• pp.1218-1226
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• 1999

In this paper, the extended Biot's semilinear model was developed. Combining the extended Biot model with the dynamic equation yields the nonlinear wave equation in poproelastic sound absorbing materials. Both perturbation and matching techniques are used to find solutions for nonlinear wave equations. By comparing results between linear and nonlinear wave solutions, characteristics of nonlinear waves in poroelastic sound abosrbing materials have been studied. Nonlinear waves were found to be attenuated faster than the linear ones. A maximum amplitude of the nonlinear wave occurred near its surface boundaries and decay quickly with distance from the surface. It has also been found that, if the amplitudes of linear waves are known at the surface boundaries, those of nonlinear ones can be determined. This will be the basis of finding effects of nonlinearity on the absorption coefficient and the transmission loss.

• Journal of Ocean Engineering and Technology
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• v.14 no.2
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• pp.1-6
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• 2000

Wave energy absorption by a flap equipped with a harbor in a water of finite depth is studied. The wave potential is calculated by a hybrid integral equation consisting of Green integral equations associated with Rankine and Kelvin Green functions. The absorbed wave energy is calculated by both the near-field and far-field methods. The present methods can be used for the design of a flap-harbor wave energy absorber since the numerical results by the two methods are in good agreement.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.649-654
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• 2017

In this note, we seek traveling wave solutions of a shallow water model in a one dimensional space by a simple but rigorous calculation. From the profile equation of traveling wave solutions, we need to investigate the phase portrait of a one dimensional ordinary differential equation $\tilde{u}^{\prime}=F(\tilde{u})$ connecting two end states of the traveling wave solution.

• Journal of Ocean Engineering and Technology
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• v.11 no.2
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• pp.77-90
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• 1997

Wave deformation due to Oscillating water column (OWC) plant was studied. To solve this problem, three dimensional numerical method based on Improved Green integral equation was applied. Method condition was considered as well as fixed condition and freely floating condition. From the calculation results, main characteriatic of wave deformation due to OWC plant were discussed. Also, some calculations for the floating barge were performed to confirm the validity of numerical solution of the method.

• Journal of the Korean Society for Marine Environment & Energy
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• v.12 no.3
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• pp.165-172
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• 2009

A set of equations for description of transformation of harmonic waves is proposed here. Velocity potential function and separation of variables are introduced for the derivation. The continuity equation is in a vertical plane is integrated through the water so that a horizontal one-dimensional wave equation is produced. The new equation composed of the complex velocity potential function, further be modified into. A set up of equations composed of the wave amplitude and wave phase gradient. The horizontally one-dimensional equations on the wave amplitude and wave phase gradient are the first and second-order ordinary differential equations. They are solved in a one-way marching manner starting from a side where boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient. Simple spatially-centered finite difference schemes are adopted for the present set of equations. The equations set is applied to three test cases, Booij's inclined plane slope profile, Massel's smooth bed profile, and Bragg's wavy bed profile. The present equations set is satisfactorily verified against existing theories including Massel's modified mild-slope equation, Berkhoff's mild-slope equation, and the full linear equation.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.631-649
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• 2019

In this paper, we prove the global nonexistence of solutions for a quasilinear wave equation with time delay and acoustic boundary conditions. Further, we establish the blow up result under suitable conditions.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.289-291
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• 2005

In this paper, we introduce the backward solution of nonlinear wave equation for denoising. The PDE method is approved about 4 PSNR value compare with any convolution method. In neuro images, denoising process using proposed PDE is good about 0.2% increased Voxel Region.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.