• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.819-825
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• 2016

In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.319-327
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• 2012

The equations of a multifluid interpenetration mix model are analyzed. The model is an intermediate mix model in the sense that it is defined by partial pressures but only a single global pressure and a single global temperature. It none-the-less avoids the stability difficulty. It is shown that the model is hyperbolic so that it is mathematically stable.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.193-226
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• 2001

We study Feynman's Operational Calculus for operator-valued functions of time and for measures which are not necessarily probability measures; we also permit the presence of certain unbounded operators. further, we relate the disentangling map defined within the solutions of evolution equations and, finally, remark on the application of stability results to the present paper.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.85-109
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• 2000

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.915-932
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• 2017

In this paper, we introduce a new type of additive functional equations and establish the generalized Ulam-Hyers stability for it in intuitionistic fuzzy normed space by using direct and fixed point methods.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.27-43
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• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.127-133
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• 2012

In this paper we give a necessary and sufficient condition for characterizing $h$-stability for linear dynamic systems on time scales by using Lyapunov functions.