• 대한수학회보
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• 제54권4호
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• pp.1457-1470
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• 2017

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.153-161
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• 2015

In this work, we consider an elliptic system $$\left{\array {-{\Delta}u=au+bv+{\delta}_1u+-{\delta}_2u^-+f_1(x,u,v) && in\;{\Omega},\\-{\Delta}v=bu+cv+{\eta}_1v^+-{\eta}_2v^-+f_2(x,u,v) && in\;{\Omega},\\{\hfill{70}}u=v=0{\hfill{90}}on\;{\partial}{\Omega},}$$, where ${\Omega}{\subset}R^N$ be a bounded domain with smooth boundary. We prove that the system has at least two nontrivial solutions by applying linking theorem.

• 대한수학회지
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• 제49권2호
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• pp.265-291
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• 2012

In this paper, we consider the regularity theory and the existence of smooth solution of a degenerate fully nonlinear equation describing the evolution of the rolling stones with nonconvex sides: $\{M(h)=h_t-F(t,z,z^{\alpha}h_{zz})\;in\;\{0<z{\leq}1\}{\times}[0,T] \\ h_t(z,t)=H(h_z(z,t),h)\;{on}\;\{z=0\}$. We establish the Schauder theory for $C^{2,{\alpha}}$-regularity of h.

• 대한수학회지
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• 제51권6호
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• 대한수학회지
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• 제37권3호
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• pp.339-358
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• 2000

Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .

• 대한수학회지
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• 제40권3호
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• pp.503-516
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• 2003

We show in this paper that every domain in a separable Hilbert space, say H, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz [10] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.

• 대한수학회보
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• 제31권2호
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• 호남수학학술지
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• 제31권4호
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• pp.633-637
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• 2009

We prove using the Szeg$\H{o}$ kernel and the Garabedian kernel that a Toeplitz operator on the boundary of $C^{\infty}$ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

• Journal of electromagnetic engineering and science
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• 제11권1호
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• pp.56-61
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• 2011

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

• 한국통신학회논문지
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• 제22권5호
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• pp.881-888
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• 1997

The existing method s for curvature estimation have a common problem in determining a unique smoothong factor. we previously proposed two approaches to overcome that problem: a constrained regularization approach and a mean field annealing approach. We consistently detected corners from the perprocessed smooth boundary obtained by either the constrained eglarization approach or the mean field annealing approach. Moreover, we defined corner sharpness to increase the robustness of both approaches. We evaluate the performance of those methods proposed in this paper. In addition, we show some matching results using a two-dimensional Hopfield neural network in the presence of occlusion as a demonstration of the power of our proposed methods.