• Title/Summary/Keyword: boundary condition

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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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THE EIGENVALUE PROBLEM AND A WEAKER FORM OF THE PRINCIPLE OF SPATIAL AVERAGING

  • Kwean, Hyuk-Jin
    • The Pure and Applied Mathematics
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    • v.9 no.1
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    • pp.31-37
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    • 2002
  • In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

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NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS

  • KIM, SEICK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.189-195
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    • 2015
  • The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.

A Dynamic Method for Boundary Conditions in Lattice Boltzmann method

  • Suh, Yong-Kweon;Kang, Jin-Fen;Kang, Sang-Mo
    • Proceedings of the KSME Conference
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    • 2007.05b
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    • pp.2797-2802
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    • 2007
  • It has been confirmed that implementation of the no-slip boundary conditions for the lattice-Boltzmann method play an important role in the overall accuracy of the numerical solutions as well as the stability of the solution procedure. We in this paper propose a new algorithm, i.e. the method of the dynamic boundary condition for no-slip boundary condition. The distribution functions on the wall along each of the links across the physical boundary are assumed to be composed of equilibrium and nonequilibrium parts which inherit the idea of Guo's extrapolation method. In the proposed algorithm, we apply a dynamic equation to reflect the computational slip velocity error occurred on the actual wall boundary to the correction; the calculated slip velocity error dynamically corrects the fictitious velocity on the wall nodes which are subsequently employed to the computation of equilibrium distribution functions on the wall nodes. Along with the dynamic selfcorrecting process, the calculation efficiently approaches the steady state. Numerical results show that the dynamic boundary method is featured with high accuracy and simplicity.

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Effects of Soil Conditions on the Vibratory Motion of Drilled Shaft (지반조건이 현장 타설 말뚝 선단부의 동적 경계조건에 미치는 영향)

  • 이병식;이원구
    • Proceedings of the Korean Geotechical Society Conference
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    • 2000.03b
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    • pp.159-166
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    • 2000
  • Non-destructive out-hole tests, impact-echo and impact-response are widely applied to evaluate integrity of drilled shafts. In these tests, vibratory motions of drilled shafts are interpreted, which induced by impacts on the shaft head. In applying the tests to evaluating integrity of shaft, it has been attended whether the tests have resolutions enough to distinguish existence of slime at between the shaft end and a bearing soil deposit. To distinguish existence of slime by tests, modes of shaft vibrations need to be reasonably interpreted, which generally vary according to a shaft boundary condition such as, a free-free or a free-fixed condition. The boundary condition of a shaft is, however, found to be significantly affected by stiffness of soil deposits around shaft as well as penetration depths of shaft into a bearing soil deposit. Thus, these effects on the boundary condition of a shaft should be considered reasonably in interpreting test results to decide the existence of slime. To investigate the effects, in this study, vibratory motions of shafts constructed in various soil conditions and end penetration depths are examined analytically. Based on the studies, variations of boundary condition are characterized in terms of soil stiffness contrast between a shaft perimeter and a shaft end, and also the ratio of a penetration depth to a shaft length. The results can be applied to verify the applicability of tests to identify the slime.

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On Reasonable Boundary Condition for Inclined Seabed/Structure in Case of the Numerical Model with Quadrilateral Mesh System (사각격자체계 수치모델에서의 경사면 처리기법에 관하여)

  • Hur, Dong-Soo;Lee, Woo-Dong;Bae, Ki-Seong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.5B
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    • pp.591-594
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    • 2008
  • Present study aims at the development of a reasonable boundary condition for a structure over inclined seabed in case of the numerical model with quadrilateral mesh system. The technique for the inclined impermeable/permeable boundary in the quadrilateral mesh is newly proposed. The new technique and LES-WASS-3D model (Hur and Lee, 2007) have been used for the investigation of the dynamics of fluid field, and validated through the comparison with a typical stair-type boundary condition. 3-Dimensional numerical model with Large Eddy Simulation is called LES-WASS-3D, and is able to simulate directly interaction of WAve Structure Sea bed/Sandy beach.

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