• 한국음향학회지
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• 제31권1호
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• pp.19-28
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• 2012

Kirchhoff 적분식을 이용하여 외부 음향 문제의 시간 영역 응답을 계산하는 경우, 주파수영역 해석과 마찬가지로 가상적인 내부 음향 모드에 기인한 비유일성 문제가 발생한다. 이를 해결하는 방법들 중의 하나로서 CHIEF(Combined Helmholtz Integral Equation Formulation) 방법이 쓰이는데, 이는 몇몇 내부 수음점의 응답을 0으로 추가하여 구속하는 조건을 부가하는 기법이다. 이 기법은 주파수 영역 경계요소법에서는 간편한 수식 때문에 많이 사용되고 있지만, 시간 영역에서는 사용된 예가 없다. 본 연구에서는 대상체 내부의 가상 수음점과 경계 표면의 절점들간의 최소 거리에 대한 지연시간을 고려하여, 계산하고자 하는 미지수인 현재 시간의 경계 표면 음장을 구속함으로써, 시간 영역 해석에 적합하도록 CHIEF 방법을 수식화하였다. 예제로서, 반지름 방향으로 진동하는 구의 음향 방사 문제를 다루었다. CHIEF 방법을 적용함에 따라 저차의 내부 음향 모드에 기인한 비유일성 문제를 해결할 수 있었고, 비요동 모드에 의한 수치적 불안정성을 피할 수 있었다. 그러나, 유효주파수 밖에 남은 내부 음향의 고차모드들에 의한 수치적 불안정성은 증가하였다.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.111-127
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• 2011

We prove the uniqueness solvability of the Tricomi problem for the elliptic - hyperbolical equation of the second type by using a new representation of the solution in the generalized class R.

• 대한수학회논문집
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• 제38권2호
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• pp.575-588
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• 2023

In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an n-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.79-91
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• 2010

In this paper, a class of fractional integrodifferential equations of mixed type with nonlocal conditions is considered. First, using contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. Second, the existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with nonlocal conditions is also presented.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• 대한수학회지
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• 제48권4호
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• pp.867-885
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• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• 대한수학회지
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• 제44권2호
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• pp.443-453
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• 2007

We study the equation of a membrane with strong viscosity. Based on the variational formulation corresponding to the suitable function space setting, we have proved the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• 대한수학회지
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• 제54권3호
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• pp.945-966
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• 2017

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.335-354
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• 2007

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (${\hat}It{o}$ type) stochastic integrals with respect to the generalized Wiener process and prove the ${\hat}It{o}$ formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.