• 대한수학회지
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• 제59권6호
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• 자연과학논문집
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• 제8권2호
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• pp.9-11
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• 1996

Dirichlet 경계조건을 갖는 Laplace 고유치방정식의 고유치를 구하는 데 복합마디방법을 이용하였다. 유한차분법을 적용하여 행렬 고유치방정식을 만들고 이 방정식의 고유치를 구하기 위하여 역거듭제곱방법과 전체복합마디법을 사용하였다. 그 결과 고유치를 기존의 방법보다 더욱 빠르게 구할 수 있었다.

• 대한수학회보
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• 제49권4호
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• pp.669-684
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• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.243-248
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• 1997

A full multigrid scheme was used in computing some eigenvalues of the Laplace eigenvalues problem with the Dirichlet bound-ary condition. We get a system of algebraic equations with an aid of finite difference method and apply subspace iteration method to the system to compute first some eigenvalues. The result shows that this is very effective in calculating some eigenvalues of this problem.

• Nuclear Engineering and Technology
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• 제28권3호
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• pp.311-319
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• 1996

We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

• 대한수학회지
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• 제49권4호
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• 대한토목학회논문집
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• 제9권3호
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• pp.97-106
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• 1989

본(本) 연구(硏究)는 유한요소법(有限要素法)(FEM)을 이용(利用)하여 2차원(次元) 지하수(地下水) 흐름모형(模型)을 확립(確立)한 것으로 지하수계(地下水界)에서의 오염물질이동(汚染物質移動)에 관한 종합적(綜合的)인 동적(動的)시스템 모형(模型)을 개발(開發)하는 연구(硏究)의 첫 단계(段階)이다. 이 흐름모형(模型)은 보다 많은 실재문제(實在問題)를 다를 수 있는 융통성(融通性)과 유연성(柔軟性)을 가지도록 하고 있다. 시간(時間)의 함수(函數)로 나타나는 Sources/Sinks, Dirichlet 형(形)의 경계조건(境界條件), Neumann 형(形) 혹은 Cauchy 형(形)의 유동(流動) 경계조건(境界條件), 누수성피압상(漏水性被壓床) (leaky confining beds) 등(等)의 조건(條件)을 가진 지하수(地下水)흐름을 모의발생(模擬發生 수 있으며, 또 복잡(複雜)한 경계조건(境界條件)을 잘 나타내기 위하여 삼각형요소(三角形要素)와 사각형요소(四角形要素)를 혼합(混合)하여 쓸 수 있는 지하수(地下水)흐름 FEM 모형(模型)을 확립(確立)한 것이다.