• 대한수학회지
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• 제37권6호
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• 대한수학회지
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• 제38권4호
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• pp.781-791
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• 2001

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.419-430
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• 2016

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

• 대한수학회보
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• 제57권3호
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• pp.597-605
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• 2020

In this article, we discuss the global uniqueness problem for the Radon transform. It is not sufficient for the global uniqueness for the Radon transform to assume that the Radon transform Rf for a function f absolutely converges on any hyperplane. It is also known that it is sufficient to assume that f ∈ L¹ for the global uniqueness to hold. There exists a big gap between the above two conditions, to fill which is our purpose in this paper. We shall give a better sufficient condition for the global uniqueness of the Radon transform.

• 한국산학기술학회논문지
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• 제11권7호
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• pp.2328-2333
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• 2010

직접경계요소법은 음향방사문제 해석에 널리 적용되는 수치해석기법중 하나이지만, 외부 음향방사 문제에 있어서는 방사면 내부공간의 고유주파수 근방에서 비유일성이 나타나게 된다. 이를 해결하기 위한 방법으로 CHIEF 방법이 일반적으로 적용되어 왔으며, 최근 들어서는 ICA-Ring 방법과 같은 새로운 기법이 제안되어 해의 정확도 향상에 기여하고 있다. 본 논문에서는 앞서 언급한 두 가지 비유일성 회피기법들의 특성을 살피고, 각각의 기법 구현을 포함한 직접경계요소법 기반의 수치해석 코드를 작성한다. 또한, 법선방향 균일속도로 진동하는 구의 음향방사문제에 대한 수치해석을 수행하고 그 결과를 해석 해와 비교하여 각각의 기법들에 대한 비유일성 회피 성능을 고찰한다.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.771-777
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• 2009

In this paper, we study the uniqueness problem on entire functions sharing fixed points and prove some theorems which are related to one famous problem of Hayman.

• 대한수학회논문집
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• 제17권4호
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• pp.593-606
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• 2002

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.349-356
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• 2005

In this paper, by using the Leray-Schauder continuation theorem and Wirtinger-type inequalities, we establish the existence and uniqueness theorems for two-point boundary value problems of a certain class of fourth-order nonlinear differential equations.

• 대한수학회논문집
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• 제16권3호
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• pp.405-413
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• 2001

The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.57-68
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• 2007

In this article, we investigate the problem of uniqueness of meromorphic functions sharing one set and having deficient values, and obtain a result which improves some earlier results.