• Title, Summary, Keyword: Dirichlet boundary condition

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On the Reconstruction of Pinwise Flux Distribution Using Several Types of Boundary Conditions

  • Park, C. J.;Kim, Y. H.;N. Z. Cho
    • Nuclear Engineering and Technology
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    • v.28 no.3
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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.

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MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A NONLINEAR PARABOLIC EQUATION UNDER DIRICHLET BOUNDARY CONDITION

  • Choi, Q-Heung;Jin, Zheng-Guo
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.697-710
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    • 2000
  • We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

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EFFECT OF THE BOUNDARY CONDITION OF REDISTANCE EQUATION ON THE LEVEL SET SOLUTION OF SLOSHING PROBLEM (Redistance 방정식의 경계조건이 슬로싱 문제의 level set 해석에 미치는 영향)

  • Choi, H.G.
    • 한국전산유체공학회:학술대회논문집
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    • pp.165-169
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    • 2009
  • The effect of the Dirichlet boundary condition for the redistance equation of level set method on the solutionof sloshing problem is investigated by adopting four Dirichlet boundary conditions. For the solution of the incompressible Navier-Stokes equations, P1P1 four-step fractional finite element method is employed and a least-square finite element method is used for the solutions of the two hyperbolic type equations of level set method; advection and redistance equation. ALE (Arbitrary Lagrangian Eulerian) method is used to deal with a moving computational domain. It has been shown that the free surface motion in a sloshing tank is strongly dependent on the type of the Dirichlet boundary condition and the results of broken dam and sloshing problems using various Dirichlet boundary conditions are discussed and compared with the existing experimental results.

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MULTIPLE SOLUTIONS FOR THE SYSTEM OF NONLINEAR BIHARMONIC EQUATIONS WITH JUMPING NONLINEARITY

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.551-560
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    • 2007
  • We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.

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NOTE ON LOCAL ESTIMATES FOR WEAK SOLUTION OF BOUNDARY VALUE PROBLEM FOR SECOND ORDER PARABOLIC EQUATION

  • Choi, Jongkeun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1123-1148
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    • 2016
  • The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

THE NON-EXISTENCE OF HOPE BIFURCATION IN A DOUBLE-LAYERED BOUNDARY PROBLEM SATISFYING THE DIRICHLET BOUNDARY CONDITION

  • Ham, Yoon-Mee
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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    • pp.441-447
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    • 1999
  • A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

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ON THE EXISTENCE OF THE THIRD SOLUTION OF THE NONLINEAR BIHARMONIC EQUATION WITH DIRICHLET BOUNDARY CONDITION

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.81-95
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    • 2007
  • We are concerned with the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=g(u)$, in ${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show that there exists at least three solutions of the above problem under the suitable condition of g(u).

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