• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.477-486
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• 2000

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x+y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on restricted (unbounded) domains.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.825-841
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• 2020

We characterize bicomplex holomorphic functions from several estimates. Originally, Riley [5] studied such problems in local case. In our study, we treat global estimates on various unbounded domains. In many cases, we can determine the explicit form of a function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.107-127
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• 2014

The goal of this note is to describe the asymptotic behaviour of problems set in cylinders when the size of them is becoming infinite. This leads to consider problems in unbounded domains as well as new singular perturbations issues.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1439-1470
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• 2022

In this paper, we study the uniform attractor of the 2D nonautonomous tropical climate model in an arbitrary unbounded domain on which the Poincaré inequality holds. We prove that the uniform attractor is compact not only in the L²-spaces but also in the H¹-spaces. Our proof is based on the concept of asymptotical compactness. Finally, for the quasiperiodical external force case, the dimension estimates of such a uniform attractor are also obtained.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.751-761
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• 2000

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.59-71
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• 2018

We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.47-66
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• 2009

Radiation damping due to wave propagation in unbounded domains may cause a significant reduction of structural vibrations when excited near resonance. Here a novel matrix-valued algebraic Pad$\acute{e}$-like stiffness formulation in the frequency-domain and a corresponding state equation in the time domain are elaborated for a soil-structure interaction problem with a layered soil excited in a transient manner by a flexible rotor during startup and shutdown. The contribution of radiation damping caused by a soil-layer upon a rigid bedrock is characterized by the corresponding amount of critical damping as it is used in structural dynamics.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.33-38
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• 2008

For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. Paraxial boundary conditions(PBCs) which are kinds of absorbing boundary conditions based on paraxial approximations of the scalar and elastic wave equations not only lead to well-posed problem but also are stable and computationally inexpensive. But the complex mathematical forms of PBCs with partial derivatives complicate the application of those to finite element analysis. In this paper a penalty functional is newly proposed for applying PBCs into finite element analysis and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The numerical verification of the efficiency is carried out through comparing PBCs with a viscous boundary condition.