• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권2호
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• pp.73-86
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• 2009

The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using the variational method technique. The problem is characterized by two parameters: the Nusselt number(N) and the dynamic parameter($\Lambda$). We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.143-154
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• 2003

Analytical solutions for the viscous Cahn-Hilliard equation are considered. Existence and uniqueness of the solution are shown. The exponential decay of the solution in H$^2$-norm, which is an improvement of the result in Elliott and Zheng[5]. We also compare the early stages of evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation, which has been given as an open question in Novick-Cohen[8].

• Steel and Composite Structures
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• 제25권3호
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• pp.347-360
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• 2017

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

• 대한수학회논문집
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• 제32권3호
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• East Asian mathematical journal
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• 제34권5호
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• pp.633-641
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• 2018

A viscoelastic wave equation in canonical form weakly nonlinear time dependent dissipation and source terms is investigated in this paper. And we establish a general decay result which is not necessarily of exponential or polynomial type.

• 제어로봇시스템학회논문지
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• 제19권7호
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• pp.583-586
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• 2013

We consider discrete-time LTI (Linear Time-Invariant) systems with constant input delays. The input delay is modeled by a first-order PdE (Partial difference Equation) and a backstepping transformation is employed to design a predictor feedback controller. The backstepping approach results in the construction of an explicit Lyapunov function, with which we prove the exponential stability of the closed-loop system formed by the predictor feedback. The numerical example demonstrates the design of the predictor feedback controller, and illustrates the validity of the exponential stability.

• 대한수학회지
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• 제56권3호
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• pp.825-855
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• 2019

We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.

• 공업화학
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• 제7권2호
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• pp.356-361
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• 1996

반응성 첨가제로 HQ와 PGE를 합성시킨 HQ-PGE를 사용하여, DGEBA/MDA계의 경화반응이 일어날 때의 속도론을 DSC와 FT-IR을 이용하여 조사하였다. 그리고, Kissinger equation과 Arrhenius equation을 이용하여 활성화 에너지와 pre-exponential factor 값을 구하였다. 계의 활성화 에너지는 HQ-PGE가 첨가되었을 때 감소하였다. 합성 HQ-PGE가 5 phr 첨가되었을 때, DGEBA/MDA계의 활성화 에너지는 FT-IR로 측정하였을 때 7.8 kcal/mol, DSC로 측정하였을 때에 11.3 kcal/mol을 나타내었다. 이 값은 HQ-PGE가 첨가되지 않은 경우보다 각각 30%, 9% 감소된 값이었다. 이 결과들을 통해서 반응성 첨가제로 사용된 HQ-PGE는 본 계에서 촉매의 역할을 함을 알 수 있었다.

• Steel and Composite Structures
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• 제23권6호
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• pp.657-668
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• 2017

In the most of previous studies, researchers have restricted their own studies to consider the effect of single walled carbon nanotubes as a reinforcement on the vibrational behavior of structures. In the present work, free vibration characteristics of functionally graded annular plates reinforced by multi-walled carbon nanotubes resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of the multi-walled carbon nanotube/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the multi-walled carbon nanotubes wt% range considered. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the plates are investigated. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of annular plates.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2009년도 학술발표회 초록집
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• pp.1306-1310
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• 2009

The roughness coefficients were estimated by the Manning's equation for the measured stage and flow velocity of Bocheong stream basin in Kum river. The relationships between the estimated roughness coefficients and the geomorphologic factors were formulated by the linear, logarithmic, exponential and power type function, thereafter correlation equations were presented. The correlation analysis was performed between the measured stream length and the basin area of Bocheong stream basin by the linear, logarithmic, exponential and power type function, and correlation equation for the stream length was given. The roughness coefficient has strong correlationship with stream slope, but low correlation coefficients with stream length and basin area. For the correlationship with the roughness coefficients and the stream slope, the logarithmic type function has the smallest correlation coefficient, on the other hand, the exponential type function has the largest correlation coefficient. For the relationship between the stream length and the basin area, the correlation coefficient of the logarithmic type function shows the smallest value, linear type function shows the largest value.