• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.953-966
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• 2010

In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.247-259
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• 2003

Optimal control problem for the exploitaton of oil is investigated. The optimal control problem under consideration in this paper is governed by weak coupled parabolic PDEs and involves with pointwise state and control constraints. The properties of solution of the state equations and the continuous dependence of state functions on control functions are investigated in a suitable function space; existence of optimal solution of the optimal control problem is also proved.

• Transactions of the Korean hydrogen and new energy society
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• v.30 no.4
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• pp.376-383
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• 2019

This paper presents of thermal performance analysis by using mathematical models for a compound parabolic collector (CPC) system employing heat storage tank. The thermal performance including insolation energy, heat loss from collector system, useful energy, collector efficiency, and temperature of storage tank were theoretically investigated through a year using monthly-average meteorological data at Seoul. The simulated results showed that the CPC systems are suitable for the applications of higher temperature than flat plate collector (FPC) systems.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.787-796
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• 2015

When the temperature of a structure varies, there is a tendency to produce changes in the shape of the structure. The resulting actions may be of considerable importance in the analysis of the structures having non-prismatic members. The computation of design forces for the non-prismatic beams having symmetrical parabolic haunches (NBSPH) is fairly difficult because of the parabolic change of the cross section. Due to their non-prismatic geometrical configuration, their assessment, particularly the computation of fixed-end horizontal forces and fixed-end moments becomes a complex problem. In this study, the efficiency of the Artificial Neural Networks (ANN) and Adaptive Neuro Fuzzy Inference Systems (ANFIS) in predicting the design forces and the design moments of the NBSPH due to temperature changes was investigated. Previously obtained finite element analyses results in the literature were used to train and test the ANN and ANFIS models. The performances of the different models were evaluated by comparing the corresponding values of mean squared errors (MSE) and decisive coefficients ($R^2$). In addition to this, the comparison of ANN and ANFIS with traditional methods was made by setting up Linear-regression (LR) model.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Kyungpook Mathematical Journal
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• v.16 no.2
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• pp.225-229
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• 1976

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.16.1-16
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• 2002

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.4
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• pp.388-396
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• 2011

Sun tracking system is the most important subsystem in parabolic dish type solar thermal power plant, since it determines the amount of thermal energy to be collected, thus affects the efficiency of solar thermal power plant most significantly. Various types of sun tracking systems are currently used. Among them, use of photo sensors to located the sun(which is called sensor type) and use of astronomical algorithm to compute the sun position(which is called program type) are two of the mostly used methods. Recently some uses CCD sensor, like CCD camera, which is called image processing type sun tracking system. This work is concerned with the analysis of sun tracking performance of various types of sun tracking systems currently used in the parabolic dish type solar thermal power plant. We first developed a sun tracking error measurement system. Then, we evaluate the performance of five different types of sun tracking systems, sensor type, program type, hybrid type(use of sensor and computed sun position simultaneously), tracking error compensated program type and image processing type. Experimentally obtained data shows that the tracking error compensated program type sun tracking system is very effective and could provide a good sun tracking performance. Also the data obtained shows that the performance of sensor type sun tracking system is being affected by the cloud significantly, while the performance of a program type sun tracking system is being affected by the sun tracking system's mechanical and installation errors very much. Finally image processing type sun tracking system can provide accurate sun tracking performance, but costs more and requires more computational time.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.67-86
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• 2014

Based on an expanded mixed finite element method, we consider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on ${\Omega}{\subset}R^d$, $1{\leq}d{\leq}3$. We construct the semidiscrete approximations of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u in $L^2$ normed space.