Displaying similar documents to “Eliciting harmonics on strings”

The geometrical quantity in damped wave equations on a square

Pascal Hébrard, Emmanuel Humbert (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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The energy in a square membrane subject to constant viscous damping on a subset ω ⊂ Ω decays exponentially in time as soon as satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate τ ( ω ) of this decay satisfies τ ( ω ) = 2 min ( - μ ( ω ) , g ( ω ) ) (see Lebeau [ (1996) 73–109]). Here μ ( ω ) denotes the spectral abscissa of the damped wave equation operator and  g ( ω ) is a number called the geometrical quantity of and defined as follows. A ray in is the trajectory generated by the free...

Stabilization of Timoshenko beam by means of pointwise controls

Gen-Qi Xu, Siu Pang Yung (2003)

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...