• 대한수학회지
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• 제45권5호
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• pp.1361-1378
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• 2008

This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권2호
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• pp.85-91
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Gannesh C. Gorain [1]. Energy decay rates are obtained by the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• 제28권3호
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• pp.339-345
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchho type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• 제30권3호
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• pp.249-258
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• 2014

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang[14]. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

• 대한수학회지
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• 제43권3호
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• pp.659-676
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• 2006

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

• 대한수학회논문집
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• 제11권2호
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• pp.515-523
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• 1996

We prove that vicosity solutions are stabel under changes in the flux functions as well as boundary functions. This result can be used in the study of numerical approximation of Hamilton-Jacobi equations.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.47-62
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• 1997

This paper is concerned with investigating the global as-ymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation, Moreover an esti-mate of the rate of decay of the solutions is obtained.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.517-527
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• 2016

In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

• Structural Engineering and Mechanics
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• 제24권6호
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• pp.709-725
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• 2006

In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

• Wind and Structures
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• 제20권1호
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• pp.15-36
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• 2015

Characterization of wind flows over a complex terrain, especially mountain-gorge terrain (referred to as the very complex terrain with rolling mountains and deep narrow gorges), is an important issue for design and operation of long-span bridges constructed in this area. In both wind tunnel testing and numerical simulation, a transition section is often used to connect the wind tunnel floor or computational domain bottom and the boundary top of the terrain model in order to generate a smooth flow transition over the edge of the terrain model. Although the transition section plays an important role in simulation of wind field over complex terrain, an appropriate shape needs investigation. In this study, two principles for selecting an appropriate shape of boundary transition section were proposed, and a theoretical curve serving for the mountain-gorge terrain model was derived based on potential flow theory around a circular cylinder. Then a two-dimensional (2-D) simulation was used to compare the flow transition performance between the proposed curved transition section and the traditional ramp transition section in a wind tunnel. Furthermore, the wind velocity field induced by the curved transition section with an equivalent slope of $30^{\circ}$ was investigated in detail, and a parameter called the 'velocity stability factor' was defined; an analytical model for predicting the velocity stability factor was also proposed. The results show that the proposed curved transition section has a better flow transition performance compared with the traditional ramp transition section. The proposed analytical model can also adequately predict the velocity stability factor of the wind field.