• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.420-424
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• 1993

New conditions for the exponential stability for both linear nonautnomous finite and a class of infinite dimensional systems described by parabolic partial differential equations (PDE's) are derived. The results for the parabolic systems are derived via semigroup approach.

• East Asian mathematical journal
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• v.26 no.3
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• pp.403-413
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• 2010

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.303-316
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• 2000

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

• Steel and Composite Structures
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• v.50 no.1
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• pp.25-43
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• 2024

In this article, a mathematical model is developed to predict the dynamic behavior of bio-inspired composite beam with helicoidal orientation scheme under variable axial load using a unified higher order shear deformation beam theory. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equation of composite beam is proposed based on plane stress problem. The variable axial load is distributed through the axial direction by constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived in detail by Hamilton's principle. Using the differential quadrature method (DQM), the governing equations, which are integro-differential equations are discretized in spatial direction, then they are transformed into linear eigenvalue problems. The proposed model is verified with previous works available in literatures. Parametric analyses are developed to present the influence of axial load type, orthotropic ratio, slenderness ratio, lamination scheme, and boundary conditions on the natural frequencies of composite beam structures. The present enhanced model can be used especially in designing spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.25-34
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• 2003

We prove a local unique continuation for Schr$\ddot{o}$dinger equations with time independent coefficients. The method of proof combines a technique of Fourier-Gauss transformation and a Carleman inequality for parabolic operator.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.2
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• pp.66-75
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• 1989

Simple formulas for evaluating the radiation characteristics of an offset parabolic antennas are presented. The validity of the proposed equations was verified by comparing the results wit the numerical clculation. The offset parabolic antenna for the domestic broadcasting satellite has been designed by using of simple formulas. The radiation patterns of the desinged offset parabolic antenna show good agreement with experimental results.

• Advances in Energy Research
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• v.4 no.4
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• pp.299-323
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• 2016

Cylindrical parabolic solar concentrators of small concentration ratio are attractive options for working temperatures around $120^{\circ}C$. The heat gained can be utilized in many applications such as air conditioning, space heating, heating water and many others. These collectors can be easily manufactured and do not need to track the sun continuously. Using a heat pipe as a solar absorber makes the system more compact and easy to install. This study is devoted to modeling a system of cylindrical parabolic solar concentrators of small concentration ratio (around 5) fitted with a heat pipe absorber with a porous wick. The heat pipe is surrounded by evacuated glass tube to reduce thermal losses from the heat pipe. The liquid and vapor flow equations, energy equation, the internal and external boundary conditions were taken into consideration. The system of equations was solved and the numerical results were validated against available experimental and numerical results. The validated heat pipe model was inserted in an evacuated transparent glass tube as the absorber of the cylindrical parabolic collector. A calculation procedure was developed for the system, a computer program was developed and tested and numerical simulations were realized for the whole system. An experimental solar collector of small concentration, fitted with evacuated tube heat pipe absorber was constructed and instrumented. Experiments were realized with the concentrator axis along the E-W direction. Results of the instantaneous efficiency and heat gain were compared with numerical simulations realized under the same conditions and reasonably good agreement was found.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.259-272
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• 2008

We are concerned with the robust control problem for the chemotaxis equations with predator-prey dynamics. That is, we present the existence and uniqueness of the solution. We also show the existence of the robust control and deduce the corresponding optimality conditions.