• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.735-769
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• 2019

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with a viscoelastic term. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.859-888
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• 2021

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

• 대한조선학회논문집
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• 제30권3호
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• pp.41-50
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• 1993

본 논문은 2차원 수중익 주위의 유동해석을 위하여 포텐셜을 기저로한 여러가지 패널법을 비교 한다. 각 패널에서의 특이함수의 세기는 일정하거나 선형으로 변한다고 가정하고, Neumann 및 Dirichlet의 경계조건과 함께 혼합경계조건(Robin경계조건)을 적용하여 정식화를 한후, 각 방법의 정확도를 평가 하였다. 여러가지 2차원 단면에 대한 압력분포 및 양력을 계산하고, 해석해와 비교하였다. 날카로운 뒷날과 큰 캠버값을 갖는 날개의 경우에 특히 예민하다고 알려진 날개 뒷날 부근에서의 국소오차에 대하여 집중적인 연구를 수행하였다. 비교해석 결과, 혼합 경계조건을 사용하는 정식화 방법이 가장 정확성이 높고, 수렴속도도 우수함을 밝혔다.

• 호남수학학술지
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• 제31권4호
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• pp.579-590
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• 2009

The precise form of singular functions, singular function representation and the extraction form for the stress intensity factor play an important role in the singular function methods to deal with the domain singularities for the Poisson problems with most common boundary conditions, e.q. Dirichlet or Mixed boundary condition [2, 4]. In this paper we give an elementary step to get the singular functions of the solution for Poisson problem with Neumann boundary condition or Robin boundary condition. We also give singular function representation and the extraction form for the stress intensity with a result showing the number of singular functions depending on the boundary conditions.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.81-105
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• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.