• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.145-155
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• 2007

In this paper, we show the convergence of approximate solutions to the convective porous media equation using methodology developed in [8]. First, we obtain the approximate transport equation for the given convective porous media equation. Then using the averaging lemma, we obtain the convergence.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.261-272
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• 2001

In this paper we prove the stability of the generalized quadratic equation f(x+y)+g(x-y)-2f(x)-2g(y)=0 in the spirit of Hyers, Ulam and Rassias.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.183-193
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• 2003

In this Paper, we Prove the stability Of E quadratic type functional equation (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1827-1838
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• 2015

We give some results on hyperstability for the general linear equation. Namely, we show that a function satisfying the linear equation approximately (in some sense) must be actually the solution of it.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.731-737
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• 2024

In this paper, we study the Hyers-Ulam stability of the classical iterative functional equation fⁿ(x) = x, the Babbage equation, using strictly monotonic approximate solutions on a real interval.

• Proceedings of the Korean Fiber Society Conference
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• 2003.04a
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• pp.103-106
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• 2003

원형의 물체에 접해 있는 섬유 또는 실의 장력에 관하여 기존의 capstan equation의 잘못된 점을 보완하는 일반적인 capstan Equation을 유도하였다. 해석은 주로 섬유-물체의 접촉부위에 초점을 맞추었다. 그 결과 유도된 지배방정식은 2차 상미분 방정식의 형태를 갖는다. 지배방정식의 해를 구한 뒤, 접촉영역 전체에 작용하는 힘의 평형조건을 이용하여 입력 장력(incoming tension)과 출력 장력(outgoing tension)간의 관계식을 얻을 수 있었으며 우리는 이것을 True capstan equation이라 명하였다. (중략)

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1185-1199
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• 2015

This paper is concerned with the optimal control problem for the viscous weakly dispersive Benjamin-Bona-Mahony (BBM) equation. We prove the existence and uniqueness of weak solution to the equation. The optimal control problem for the viscous weakly dispersive BBM equation is introduced, and then the existence of optimal control to the problem is proved.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.481-487
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• 1998

Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.173-187
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• 2013

This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.