• Title/Summary/Keyword: boundary condition

Search Result 2,028, Processing Time 0.208 seconds

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

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.20 no.4
    • /
    • pp.551-560
    • /
    • 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.

  • PDF

Good Choice of Positions and Impedances of Absorptive Materials for Effective Interior Noise Control (흡음재의 적절한 위치 및 임피던스 선정을 통한 효율적인 실내 소음 제어)

  • 조성호;김양한
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • 2003.05a
    • /
    • pp.791-796
    • /
    • 2003
  • Some basic guidelines for changing non-uniform boundary condition in an acoustically small cavity are presented. In this paper, modal summation technique is used to represent inside sound field. From this formulation, corner effect is defined and proposed. The corner in a cavity is good position for changing boundary condition effectively. Impedance circle with same absorption coefficient is defined to find appropriate impedance of absorptive material for better noise control performance.

  • PDF

ERROR ANALYSIS OF FINITE ELEMENT APPROXIMATION OF A STEFAN PROBLEM WITH NONLINEAR FREE BOUNDARY CONDITION

  • Lee H.Y.
    • Journal of applied mathematics & informatics
    • /
    • v.22 no.1_2
    • /
    • pp.223-235
    • /
    • 2006
  • By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

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
    • /
    • v.14 no.2
    • /
    • pp.441-447
    • /
    • 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.

  • PDF

Normal Mode Vibrations of a Beam with a Nonlinear Boundary Condition (비선형 경계조건을 가진 보의 정규모드진동)

  • 김현기;이원경
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • 1998.04a
    • /
    • pp.392-398
    • /
    • 1998
  • In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

  • PDF

Study of Diffusion-controlled Processes. Solution of the Smoluchowski Equation with a Step Potential

  • Kim, Dae-Young;Shin, Seok-Min;Shin, Kook-Joe
    • Bulletin of the Korean Chemical Society
    • /
    • v.7 no.4
    • /
    • pp.271-275
    • /
    • 1986
  • The Smoluchowski equation with a step potential is solved in one-dimensional case and three-dimensional case with spherical symmetry. Exact analytic expressions for the solution and the remaining probability are obtained in one-dimensional case for the reflecting boundary condition and the long time behavior of the remaining probability is compared with the earlier work. In three-dimensional case, only the long time behavior is evaluated. More general case with the radiation boundary condition is also investigated and the results are shown to approach correct limits of the reflecting boundary condition.

Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

  • Jeong Ho-Eyoul;Jeong Jae-Tack
    • Journal of Mechanical Science and Technology
    • /
    • v.20 no.1
    • /
    • pp.158-166
    • /
    • 2006
  • Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

A Study on the Numerical Stability and Accuracy of Lattice Boltzmann Method with Non-equilibrium first order extrapolation boundary condition (비평형 1 차 외삽 경계조건을 이용한 격자 볼츠만 법의 수치적 안정성 및 정확도에 관한 연구)

  • Jeong, Hae-Kwon;Kim, Las-Sung;Lee, Hyun-Goo;Ha, Man-Yeong
    • Proceedings of the KSME Conference
    • /
    • 2007.05b
    • /
    • pp.2684-2689
    • /
    • 2007
  • Non-equilibrium first order extrapolation boundary condition proposed by Guo et $al.^{(9)}$ proposed has a good application for complex geometries, a second order accuracy and a treatment on non-slip wall boundary condition easily. However it has a lack of the numerical stability from high Reynolds number. Guo et $al.^{(9)}$ substituted the density value of adjacent nodes for the density of boundary nodes. This procedure causes the numerical instability on the boundary. In this paper, we derived a procedure of density extrapolation and compared to previous results.

  • PDF

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
    • /
    • 2009.04a
    • /
    • pp.165-169
    • /
    • 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.

  • PDF

Dependence of Optical Matrix Elements on the Boundary Conditions of the Continuum States in Quantum Wells

  • Jang Y. R.;Yoo K. H.;Ram-Mohan L. R.
    • Journal of the Optical Society of Korea
    • /
    • v.9 no.2
    • /
    • pp.39-44
    • /
    • 2005
  • Unlike for the bound states, several different boundary conditions are used for the continuum states above the barrier in semiconductor quantum wells. We employed three boundary conditions, infinite potential barrier boundary condition, periodic boundary condition and scattering boundary condition, and calculated the local number of states, wavefunctions and optical matrix elements for the symmetric and asymmetric quantum wells. We discussed how these quantities are related in the three boundary conditions. We argue that the scattering boundary condition has several advantages over the other two cases. These results would be useful in understanding quantum well lasers and detectors involving continuum states.