• 대한수학회지
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• 제47권6호
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• pp.1317-1328
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• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 춘계 학술발표회 논문집
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• pp.177-184
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• 2002

Large amplitude sloshing can occur in contained fluid region due to the seismic ground motion. Also, The pressure by large amplitude sloshing damages the connections between the wall and roof of a fluid container and causes outflow of contained fluid. Therefore, to predict the dynamic behavior accurately, three dimensional analysis with the nonlinear boundary condition must be performed. In this study, the numerical solution procedure is developed using the boundary element method with the Lagrangian particle approach. In order to demonstrate the accuracy and validity of the developed method, the fluid motion for a free oscillation with small amplitude and a forced vibration are analyzed. And the numerical results are compared with the linear theory results and the previous studies with the nonlinear boundary condition.

• 대한조선학회논문집
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• 제41권4호
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• pp.38-44
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• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• Korean Journal of Mathematics
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• 제22권2호
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• pp.355-365
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• 2014

We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

• 호남수학학술지
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• 제27권4호
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• pp.609-619
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• 2005

We are concerned with the multiplicity of solutions of the nonlinear elliptic equation with Dirichlet boundary condition. We reveal the existence of m solutions of the nonlinear elliptic equation by a critical point theory, under some condition.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권1호
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• pp.19-30
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• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Journal of Advanced Research in Ocean Engineering
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• 제1권3호
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.101-113
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• 2000

In this paper, we study controllability of nonlinear delay parabolic equa-tions with nonlocal initial condition under boundary input.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.135-143
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• 2008

We investigate the existence of nontrivial solutions of the nonlinear biharmonic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\Delta}^2{\xi}+c{\Delta}{\xi}={\mu}h({\xi}+{\eta})\;in{\Omega},\\{\Delta}^2{\eta}+c{\Delta}{\eta}={\nu}h({\xi}+{\eta})\;in{\Omega},\end{array}$$ where $c{\in}R$ and ${\Delta}^2$ denote the biharmonic operator.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.165-172
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• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.