• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.575-588
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• 2023

In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an n-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.1
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• pp.61-68
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• 2005

In this study, it was proposed that an equation for predicting consolidation settlement on soft clay ground, which separate total settlement into primary and secondary consolidation settlement equation. The consolidation settlements by the proposed equation and by the measured settlements from laboratory model test were compared and verified for its application. It was appeared that the proposed equation from the laboratory model test approach to be more realistic comparing to !the result of Terzaghi's equation. From the above application, it was concluded that the final settlement prediction by. the Hyperbolic, Asaoka methods is needed to the initial settlement but the proposed equation could be much applicable in the lacking condition of measured data of the initial period.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.681-692
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• 2002

In the article [2], the conjugate Darboux-Protter problem Dn is formulated for the two dimensional wave equation in the class of unbounded functions and the uniqueness of solutions has been established. In this paper, we shall show the existence of solutions for the hyperbolic equations with Bessel operators in another special case.

• Korean Journal of Hydrosciences
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• v.2
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• pp.25-37
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• 1991

The numerical models of the parabolic equation, applicable only to the progressive wave, and hyperblic equation, which may consider even the reflected wave, were developed and applied to the area of the submerged circular shoal and then results obtained from both models were compared with experimental measurements and each other. The hyperbolic model was further applied to both the detaced breakwater and the breakwater with a gap. The numerical results were plotted and compated with the existing data. Numerical solutions were obtained with the finite difference method.

• Water Engineering Research
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• v.5 no.4
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• pp.177-183
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• 2004

This paper introduces an eigenvalue method of transforming the hyperbolic partial differential equations of a particular unsteady friction water hammer model into characteristic form. This method is based on the solution of the corresponding one-dimensional Riemann problem that transforms hyperbolic quasi-linear equations into ordinary differential equations along the characteristic directions, which in this case arises as the eigenvalues of the system. A mathematical justification and generalization of the eigenvalues method is provided and this approach is compared to the traditional characteristic method.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.169-180
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• 2021

This paper investigates the time-inconsistent agent's optimal consumption and investment problem under inflation risk. The agents' discount factor is governed by hyperbolic discounting, which has a random time to change. We impose the inflation risk which plays a crucial role in long-term financial planning. We derive the semi-analytic solution to the problem of sophisticated agents when the time horizon is finite.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.197-203
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• 1998

An approach of decomposing the reflecting components is proposed by using the mild-slope equation of hyperbolic type which has the similar form to the shallow water equations. The approach is verified on Booij's problem and sinusoidally varying ripples. Inclusion of higher-order bottom effect given by chamberlain and Porter(1995) yields even more satisfactory results than the Berkhoff's mild-slope equation when compared with finite element solution or experiments.

• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.689-705
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• 2016

The Drucker-Prager yield criterion is combined with an equilibrium equation to provide the elastic-plastic stress distribution within rotating annular hyperbolic discs and the residual stress distribution when the angular speed becomes zero. It is verified that unloading is purely elastic for the range of parameters used in the present study. A numerical technique is only necessary to solve an ordinary differential equation. The primary objective of this paper is to examine the effect of the parameter that controls the deviation of the Drucker-Prager yield criterion from the von Mises yield criterion and the geometric parameter that controls the profile of hyperbolic discs on the stress distribution at loading and the residual stress distribution.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.289-298
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• 2010

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.