• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.191-202
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• 2007

By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation $$\sum_{i,j=1}^{N}D_i(a_{ij}(x){\parallel}Dy{\parallel}^{p-2}D_jy)+{\langle}b(x),\;{\parallel}Dy{\parallel}^{p-2}Dy{\rangle}+c(x)f(y)=0,\;p>1$$. The obtained theorems include and improve some existing ones for the undamped halflinear partial differential equation and the semilinear elliptic equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.387-407
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• 2015

This paper analyzes the $h{\times}p$ version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the $h{\times}p$ error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.

• Journal of the Korean Mathematical Society
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• v.7 no.1
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• pp.1-5
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• 1970

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.1
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• pp.81-90
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• 2016

The Agricultural Systems Application Platform (ASAP) provides bottom-up modelling and simulation environment for agricultural engineer. The purpose of this study is to expand usability of the ASAP to the second order partial differential equations: elliptic equations, parabolic equations, and hyperbolic equations. The ASAP is a general-purpose simulation tool which express natural phenomenon with capsulized independent components to simplify implementation and maintenance. To use the ASAP in continuous problems, it is necessary to solve partial differential equations. This study shows usage of the ASAP in elliptic problem, parabolic problem, and hyperbolic problem, and solves of static heat problem, heat transfer problem, and wave problem as examples. The example problems are solved with the ASAP and Finite Difference method (FDM) for verification. The ASAP shows identical results to FDM. These applications are useful to simulate the engineering problem including equilibrium, diffusion and wave problem.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.305-309
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• 1997

In this paper we prove the existence of a special type of multivortex solutions of $SU (N)_g \times U(1)_l$ Chern-Simons model. More specifically we prove existence of solutions of the self-duality equations for $(\Phi(x), j =1, \cdots, N$ has the same zeroes. In this case we find that the equation can be reduced to the single semilinear elliptic partial differential equations studied by Caffarelli and Yang.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1773-1778
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• 2006

Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.101-124
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• 2002

The convergence rate of a numerical procedure barred on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVP's) depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It hee been observed that the Robin condition(mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. Since the convergence rate is very sensitive to the parameter, Tang[17] suggested another interface condition called over-determined interface condition. Based on the over-determined interface condition, we formulate the two-layer multi-parameterized SAM. For the SAM and the one-dimensional elliptic model BVP's, we determine analytically the optimal values of the parameters. For the two-dimensional elliptic BVP's , we also formulate the two-layer multi-parameterized SAM and suggest a choice of multi-parameter to produce good convergence rate .

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.477-488
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• 2012

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the mixed interface condition, controlled by a parameter, can optimize SAM's convergence rate. In [8], one introduced the two-layer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. In this paper, we present a method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.383-395
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• 2016

The convergence rate of a numerical procedure based on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [8], one formulated the twolayer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. Two-dimensional implementation was presented in [10]. In this paper, we present an implementation for threedimensional problem.