• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권4호
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• pp.381-394
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• 2019

In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.

• 대한수학회보
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• 제60권6호
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• pp.1697-1704
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• 2023

We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

• 대한수학회논문집
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• 제16권3호
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• pp.509-518
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• 2001

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

• 충청수학회지
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• 제22권4호
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• pp.675-687
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• 2009

We find the multiple nontrivial solutions of the equation of the form $u_{tt}-u_{xx}=b_1[(u+1)^{+}-1]+b_2[(u+2)^{+}-2]$ with Dirichlet boundary condition. Here we reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권1호
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• pp.23-36
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• 2023

The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

• ETRI Journal
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• 제21권1호
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• pp.1-27
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• 1999

We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

• 한국해양공학회지
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• 제15권2호
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• pp.6-10
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• 2001

Water waves propagate over irregular bottom bathymetry are transformed by refraction, diffraction, shoaling, reflection etc. Principal factor of wave transform is bottom bathymetry, but in case of current field, current is another important factor which effect wave transformation. The governing equation of this study is develope as wave-current equation type to investigate the effect of wave-current interaction. It starts from Berkhoff's(1972) mild slope equation and is transformed to time-dependent hyperbolic type equation by using variational principal. Finally the governing equation is shown as a parabolic type equation by splitting method. This wave-current model was applied to the kwangan beach which is located at Pusan. The numerical simulation results of this model show the characteristics of wave transformation and flow pattern around the Kwangan beach fairly well.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.661-680
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• 2013

The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended "variational" method to solve the eigenvalue problem for the higher order dierential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunctions and eigenvalues obtained is presented. Attention is focused to find eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K[p,q]) equation.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• 지구물리와물리탐사
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• 제15권2호
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• pp.57-65
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• 2012

탄성파 수치 모형 계산에 있어서 다양한 방법들이 개발되어 적용되었다. 최근에는 특히 탄성파 수치 모형 계산에 있어 혁신적인 방법인 SEM (Spectral Element Method)가 개발되어 사용되어 왔다. 이 방법은 지형을 자유롭게 표현하는데 있어 유연한 유한요소법의 장점에 정확성을 높인 방법이다. 일반적으로 Weak Formulation 형태의 파동방정식에 육면체 요소와 Gauss-Lobatto-Legendre 적분법을 적용한 방법이 널리 사용된다. 일반적인 SEM에서는 PML (Perfectly Matched Layer)경계조건을 적용하기 어려워 속도-응력 변분식으로 파동방정식을 변경하였다. CFS-PML (Complex frequency Shifted PML)경계조건을 ADE (Auxiliary Differential Equation)방정식으로 변경하여 속도-응력 파동방정식에 적용함으로써 분리할 필요가 없는 PML을 적용한 SEM 수치 모형 계산 알고리듬을 구현하였다. 1차원 수치모형과 3차원 수치모형 실험을 통하여 SEM에 적용한 비분리 CFS-PML이 유한경계에서 인공적으로 반사되는 반사파를 효과적으로 제거하는 것을 확인하였다.