• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권4호
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• pp.295-308
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• 2016

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

• 한국해양공학회지
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• 제21권1호
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• pp.45-50
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• 2007

For a long partially-filled membrane container on an incline, the analytic solution of the similarity shape is studied. The nonlinear equation is solved and its solution is expressed as elliptic integrals, which include an unknown at the point of inflection. The point of inflection is determined by using the boundary condition at the upper separating point. Some characteristic values of the universal shape are evaluated, as the functions of inclination angle and shapes are illustrated for some cases.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.311-322
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• 2007

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

• 대한의용생체공학회:의공학회지
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• 제5권2호
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• pp.161-166
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• 1984

In this paper, we describe an effective technique for computing the steady-state motion in a two-dimensional cochlear model. With the cochlear fluid assumed incompressible and invisid, the problem reduces to solving an integral equation for a region with yielding boundary. Using the conformal mapping, Jacobian elliptic function and hyperbolic function, a pair of second-order differential equation is derived. What we will show in this paper is that by appropriately transforming integral equation, the same computation can be performed with comparable accuracy in a short time.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.41-52
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• 1998

A volume integral equation method and a mixed volume and boundary integral equation method are presented for the solution of plane elastostatic problems in solids containing orthotropic inclusions and voids. The detailed analysis of the displacement and stress fields are developed for orthotropic cylindrical and elliptic-cylindrical inclusions and voids. The accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods. Through the analysis of plane elastostatic problems in unbounded isotropic matrix containing orthotropic inclusions and voids, it is established that these new methods are very accurate and effective for solving plane elastostatic and elastodynamic problems in unbounded solids containing general anisotropic inclusions and voids or cracks.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.587-595
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• 2015

In this article, we will examine the Diophantine equation $ax^6+by^3+cz^2=0$, for arbitrary rational integers a, b, and c in Gaussian integers and find all the solutions of this equation for many different values of a, b, and c. Moreover, two equations of the type $x^6{\pm}iy^3+z^2=0$, and $x^6+y^3{\pm}wz^2=0$ are also discussed, where i is the imaginary unit and w is a third root of unity.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.237-272
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• 2021

The main purpose of the present paper is to study the asymptotic behavior near the origin of radial solutions of the equation 𝚫_p u(x) + u^q(x) + f(x) = 0 in ℝ^N\{0}, where p > 2, q > 1, N ≥ 1 and f is a continuous radial function on ℝ^N\{0}. The study depends strongly of the sign of the function f and the asymptotic behavior near the origin of the function |x|^λf(|x|) with suitable conditions on λ > 0.

• 호남수학학술지
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• 제27권2호
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• pp.205-209
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• 2005

In this paper we discuss on the uniquenss of the solution of partial differential equations: (1) $${\frac{{\partial}w}{{\partial}{\bar{z}}}}=F(z,\;w,\;{\frac{{\partial}w}{{\partial}z}}}+G(z,\;w.{\bar{w})$$ in the sobolev space $W_{1,p}(D)$.

• Structural Engineering and Mechanics
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• 제45권4호
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• pp.569-594
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• 2013

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

• 대한수학회논문집
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• 제12권2호
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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.