Weyl formula with optimal remainder estimate of some elastic networks and applications

@article{Ammari2010WeylFW,
  title={Weyl formula with optimal remainder estimate of some elastic networks and applications},
  author={Ka{\"i}s Ammari and Mouez Dimassi},
  journal={Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  year={2010},
  volume={138},
  pages={395-413}
}
Nous considerons un reseau de cordes et de poutres d'Euler-Bernoulli. En utilisant une formule de Poisson generalisee et un theoreme tauberien nous prouvons une formule de Weyl avec reste optimal. Comme consequence nous prouvons des resultats d'observabilites et de stabilisations. 
Observation of some elastic networks
Abstract We consider a network of vibrating elastic strings. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence
Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients
In this paper we consider a linear hybrid system which composed by two non-homogeneous rods connected by a point mass and generated by the equation\bea\left\{ \begin{array}{ll}

References

SHOWING 1-5 OF 5 REFERENCES
The eigenvalue problem for networks of beams
Abstract In this paper, we consider the spectral analysis of different models of networks of Euler–Bernoulli beams. We first give the characteristic equation for the spectrum. Secondly, in some
STABILIZATION OF SECOND ORDER EVOLUTION EQUATIONS BY A CLASS OF UNBOUNDED FEEDBACKS
In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates
Stabilization of Generic Trees of Strings
Abstract.We study the energy decay of a tree-shaped network of vibrating elastic strings when the pointwise feedback acts in the root of the tree. We show that the strings are not exponentially
Nicaise – “ Spectre des réseaux topologiques finis ”
  • Bull . Sci . Math .
  • 1987
Roth – “ Spectre du laplacien sur un graphe ”
  • C . R . Acad . Sci . Paris Sér . I Math .