• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.21-49
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• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• Journal of the Korean Geotechnical Society
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• v.19 no.2
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• pp.147-157
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• 2003

The characteristics of a rock joint which influence the stability of rock mass structures such as cut slopes and tunnels are largely controlled by the conditions of the rock joint as well as its boundary conditions. The conditions of rock joints comprise asperity strength, roughness, and filling materials. Boundary conditions can be represented by assuming that the deformability(or stiffness) of the rock mass surrounding the joints is modelled by a spring with stiffness. A new direct shear apparatus was developed in this study, which adapts a servo control system using PID algorithm. This apparatus can be used to investigate the various aspects of shear characteristics of the rock joints at conditions of constant normal stress and constant normal stiffness and so on. The test results for saw-cut teeth joints show that shear strength should be evaluated by considering its specific boundary conditions far the design of tunnels and cut slopes.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.41 no.3
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• pp.191-200
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• 2021

This paper deals with the boundary conditions of the stress resultants at the mid-arc for free vibration analyses of the arch. The considered arch is a horseshoe symmetric elliptic arch. The work dealing with the boundary conditions of the deflection at both ends of the arch has already been reported in the open literature. This revisited paper aims to study the suitability of the boundary conditions of the stress resultants at the mid-arc to be replaced by the boundary condition at both ends. In this study, the boundary conditions of the stress resultants at the mid-arc are newly derived based on the theory of the previous work, and natural frequencies and mode shapes are obtained using the new boundary conditions of the stress resultants. The numerical results of this paper confirm that the new boundary conditions have been validated according to previous studies and results of finite element ADINA.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.135-146
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• 1997

For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$.

• Tribology and Lubricants
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• v.14 no.3
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• pp.39-45
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• 1998

Reynolds equation, which describes behavior of fluid film in journal bearings, basically satisfies mass conservation. But, boundary conditions usually used with this equation, e.g. half Sommerfeld or Reynolds boundary conditions, cannot fulfill this natural law of conservation. In the case of connecting rod bearing, where applied load is dynamic and its magnitude is relatively large, such unrealistic boundary conditions have serious influence on calculation results, especially on lubricant flow rate or power disspation which are important parameters in thermal analysis. In this paper, mass-conserving boundary condition was applied in the finite element analysis of connecting rod bearings. Lubricant flow rate and power dissipation rate were calculated together with journal center locus, minimum film thickness and maxmium film pressure. These computation results were compared with those of the case of Reynolds boundary condition. Balance between inlet and outlet flow rate was well achieved in the case of mass-conserving boundary condition.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.04a
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• pp.212-217
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• 1998

Reynolds equation, which describes behavior of fluid film in journal bearing, basically satisfies mass conservation. But, boundary conditions usually used with this equation, e.g. half Sommerfeld or Reynolds boundary conditions, cannot fulfill this natural law of conservation. In the case of connecting rod bearing, where applied load is dynamic and its magnitude is relatively large, such unrealistic boundary conditions have serious influence on calculation results, especially on lubricant flow rate or power dissipation which are important parameters in thermal analysis. Another important factor in the analysis of connecting rod bearing is elastic deformation of bearing support structure which is relatively flexible. In this paper, EHL analysis of connecting rod beating is performed using mass-conserving boundary condition. Elastic deformation of bearing support structure and application of mass-conserving boundary condition have significant effects on the performances of connecting rod bearing.

• Steel and Composite Structures
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• v.20 no.5
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• pp.1043-1066
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• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.61-62
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• 2003

In this paper, the new higher order wall boundary conditions are proposed for solving the incompressible flows. The square driven cavity flows are simulated by using the variable order method of lines with the present wall boundary conditions. The variable order method of lines is constructed by the spatial discretization, i.e., the variable order proper convective scheme for convective terms and the modified differential quadrature method for diffusive terms, and time integration. The 2nd, 4th, and 6th order solutions are presented and these results show this higher order boundary conditions are very promising for the incompressible flow simulations.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.629-644
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• 2012

In this work, the authors study the blow-up properties of solutions to a parabolic system with nonlocal boundary conditions and nonlocal sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and precise blow-up rate estimates are also obtained.