• 대한수학회논문집
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• 제35권4호
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• pp.1143-1158
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• 2020

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source u_t - △u - △u_t = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝⁿ (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.475-487
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• 2009

This paper studies the iteration method of solving a type of second-order three-point boundary value problem with non-linear term f, which depends on the first order derivative. By using the upper and lower method, we obtain the sufficient conditions of the existence and uniqueness of solutions. Furthermore, the monotone iterative sequences generated by the method contribute to the minimum solution and the maximum solution. And the error estimate formula is also given under the condition of unique solution. We apply the solving process to a special boundary value problem, and the result is interesting.

• 한국멀티미디어학회논문지
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• 제11권12호
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• pp.1688-1696
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• 2008

We propose a hierarchical service management method using Bloom filters for large MANETs. In this paper, a MANET is comprised of logical grid hierarchy, and each mobile node within the lowest service region multicasts the Attenuated Bloom Filter (ABF) for services itself to other nodes within the region. To advertise and discovery a service efficiently, the server node of the lowest server region sends the Summary Bloom Filter (SBF) for the ABFs to the server node of upper server region. Each upper server has the set of SBFs for lower vicinity service regions. The traffic load of the proposed method is evaluated by an analytical model, and is compared with that of two alternative advertisement solutions: complete advertisement and no advertisement. As a result, we identify that the traffic load of the proposed method is much lower than that of two alternative advertisement solutions.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.39-43
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• 1996

Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 추계학술대회 학술발표 논문집
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• pp.60-64
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• 1997

In a fuzzy relation equation R=U=T, we find the bounde by U* and U* of the equation where U* is lower bound and U* is upper bound.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• 한국지반공학회논문집
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• 제27권5호
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• pp.45-59
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• 2011

본 논문은 비배수 점토지반에서 얕은 기초의 지지력계수인 $N_c$값을 도식적 상계법과 하계법을 이용해 이론적으로 유도하고 이를 Prandtl(1921)이 제안한 값과 비교하였다. 그 결과, 상계법과 하계법이 일치하는 값이 Prandtl(1921)이 제안한 $N_c$ 값이 5.14임을 확인하였으며, 유한요소해석 결과도 얕은 기초가 파괴하중에 도달할 때의 $N_c$가 5.14로 나타났다. 이러한 유한요소해석 결과는 유한요소 형태(finite e1ement type)와 수, 그리고 증분수(increments)에 크게 의존한다. 본 연구를 통해 상계법에서 구한 값과 하계법에서 구한 값이 서로 일치할 때 비로소 이론적으로 정확한 값임을 정의할 수 있으나, 일치하는 값을 유도하는 일은 매우 어려우며 일반적으로 상계법의 해와 하계법 해 사이에 존재한다고 볼 수 있다.

• 대한기계학회논문집
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• 제17권2호
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• pp.458-466
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• 1993

Natural convection in trapezoidal sections of cavity was numerically investigated using a Finite Volume Method. Temperatures of the upper inclined and lower horizontal walls are constant, with vertical side walls being insulated. When the top wall is hotter than the bottom one, a single cell of stratified flow field is obtained and heat transfer occurs only by conduction. For the colder top wall, bifurcation solutions are obtained for the higher Rayleigh numbers, while unique solutions for lower values. Flow structure is strongly dependent on the configuration and the Rayleigh number.

• 한국전산유체공학회지
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• 제21권1호
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• Structural Engineering and Mechanics
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• 제53권1호
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• pp.27-40
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• 2015

The rational analytical solutions are presented for functionally graded beams subjected to arbitrary tractions on the upper and lower surfaces. The Young's modulus is assumed to vary exponentially along the thickness direction while the Poisson's ratio keeps unaltered. Within the framework of symplectic elasticity, zero eigensolutions along with general eigensolutions are investigated to derive the homogeneous solutions of functionally graded beams with no body force and traction-free lateral surfaces. Zero eigensolutions are proved to compose the basic solutions of the Saint-Venant problem, while general eigensolutions which vary exponentially with the axial coordinate have a significant influence on the local behavior. The complete elasticity solutions presented here include homogeneous solutions and particular solutions which satisfy the loading conditions on the lateral surfaces. Numerical examples are considered and compared with established results, illustrating the effects of material inhomogeneity on the localized stress distributions.