Displaying similar documents to “On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗”

On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping

Bao-Zhu Guo, Guo-Dong Zhang (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from...

Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks

Zhong-Jie Han, Gen-Qi Xu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies...

Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks

Zhong-Jie Han, Gen-Qi Xu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies...

Stabilization of Timoshenko Beam by Means of Pointwise Controls

Gen-Qi Xu, Siu Pang Yung (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build...