• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.463-472
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• 2011

In this paper we study the solvability of parabolic equations governed by the difference of time dependent subdifferential and time independent subdifferential in reflexive Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.353-361
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• 2018

We develop a mathematical model of heat emission on the epidermis of a human body. We present a global existence theorem of solutions for a nonlinear model system of coupled partial differential equations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.703-706
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• 2005

Since soil structure interactions are one of the most important subjects in the structural/foundation engineering, much study concerning the soil structure interactions had been carried out. One of typical structures related to the soil structure interactions is the strip foundation which is basically defined as the beam or strip rested on or supported by the soils. At the present time, lack of studies on dynamic problems related to the strip foundations is still found in the literature. From these viewpoint this paper aims to theoretically investigate dynamics of the parabolic strip foundations and also to present the practical engineering data for the design purpose. Differential equations governing the free, out o plane vibrations of such strip foundations are derived, in which effects of the rotatory and torsional inertias and also shear deformation are included although the warping of the cross-section is excluded. Governing differential equations subjected to the boundary conditions of free-free end constraints are numerically solved for obtaining the natural frequencies and mode shapes by using the numerical integration technique and the numerical method of nonlinear equation.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.51-57
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• 1990

Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.19-38
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• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1179-1192
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• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.15-30
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• 1999

In this paper the second order semi-discrete and full dis-crete generalized difference schemes for one dimensional parabolic equa-tions are constructed and the optimal order $H^1$ , $L^2$ error estimates and superconvergence results in TEX>$H^1$ are obtained. The results in this paper perfect the theory of generalized difference methods.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.205-212
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• 2007

Parabolic approximation wave models based on $Pad{\acute{e}}$ approximants are analyzed in order to calculate wave transformation. In this study a $Pad{\acute{e}}(2,2)$ parabolic approximation model is developed to increase the accuracy of computation in comparison with the existing models. Numerical studies on a constant sloping bed show that the new model proves to allow for much more successful treatment of large angles of incidence than is possible using the previously available models.