• 충청수학회지
• /
• 제31권3호
• /
• pp.287-308
• /
• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권4호
• /
• pp.281-294
• /
• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• 대한수학회보
• /
• 제51권3호
• /
• pp.717-737
• /
• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• 대한수학회지
• /
• 제55권3호
• /
• pp.531-551
• /
• 2018

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

• 대한수학회보
• /
• 제39권4호
• /
• pp.589-606
• /
• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• Steel and Composite Structures
• /
• 제35권1호
• /
• pp.43-59
• /
• 2020

In this study, free vibration analysis of laminated composite parabolic thick plate frames by using finite element method is introduced. Governing equations of an eigenvalue problem are obtained from First Order Shear Deformation Theory (FSDT). Finite element method is employed to obtain natural frequency values from the governing differential equations. The frames consist of two flat square plates and one singly curved plate. Parameters like radii of curvature, aspect ratio, ply orientation and boundary conditions are investigated to understand their effect on dynamic behavior of such a structure. In addition, multi-bay structures of such geometry with different stacking order are also taken into account. The composite frame structures are also modeled and simulated via ANSYS to verify the accuracy of the present study.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제18권4호
• /
• pp.337-350
• /
• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• KIEAE Journal
• /
• 제2권3호
• /
• pp.33-38
• /
• 2002

The intermediate range of temperatures($100{\sim}300^{\circ}C$) which can be achieved with CPCs(Compound Parabolic Concentrators) without tracking device provides both economic and thermal advantages for solar collector design. The present paper summarizes critical design considerations for CPC with cylindrical absorber and its optical performance using ray tracing program. Concentration ratios vary as acceptance half angle, ratio of reflector height to aperture width and ratio of reflector area to aperture area. This effects showed that the concentration ratio was increased as acceptance angle but optimum ratio of reflector height to aperture width existed at critical value. As a result of ray tracing, solar ray losses was maximized at acceptance half angle and this problem was solved by increasing absorber tube diameter. The concentrating flux distribution on the absorber surface was uniform but peak flux existed.

• 대한토목학회논문집
• /
• 제29권2A호
• /
• pp.145-153
• /
• 2009

본 연구에서는 포물선 아치의 횡-비틂 좌굴 강도에 관한 연구를 수행하였다. 포물선 아치는 아치의 중립축을 따라 곡률이 변하므로 일정한 곡률을 갖는 원형 아치의 경우보다 횡-비틂 좌굴 강도식을 유도하는 것이 복잡하며, 이에 대한 연구가 미흡한 실정이다. 본 연구에서는 ?의 효과를 고려하여 변곡률을 갖는 아치의 횡-비틂 좌굴식을 유도하고 포물선 아치의 좌굴강도를 계산하기 위하여 유한차분법을 이용한 수치해법을 제안하였다. 이러한 수치해법은 기존 연구자 및 유한요소해석 결과와 비교하였으며, 그 타당성을 검증하였다. 마지막으로, 변수해석을 수행하여 라이즈비의 영향에 따른 원형과 포물선 아치의 횡-비틂 좌굴 강도를 비교 분석하였다.

• Structural Engineering and Mechanics
• /
• 제56권5호
• /
• pp.787-796
• /
• 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.