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

DOI10.24033/bsmf.2593zbMath1205.35304OpenAlexW4298014604MaRDI QIDQ3056514

Mouez Dimassi, Kaïs Ammari

Publication date: 12 November 2010

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://smf4.emath.fr/en/Publications/Bulletin/138/html/smf_bull_138_395-413.php

zbMATH Keywords

asymptoticseigenvaluesHilbert spaceinitial value problemeigenfunctionsTauberian theoremLebesgue measureunbounded linear operatorWeyl formulanetworks of stringsnetworks of Euler-Bernoulli beamsoptimal remainder estimates

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Plates (74K20) Asymptotic stability in control theory (93D20) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Strings (74K05) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (1)

Observation of some elastic networks

Cites Work

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• Remark on stabilization of tree-shaped networks of strings.
• Classical solvability of linear parabolic equations on networks
• Modeling, analysis and control of dynamic elastic multi-link structures
• The eigenvalue problem for networks of beams
• Stabilization of generic trees of strings
• Stabilization of star-shaped networks of strings.
• Wave propagation, observation and control in 1-\(d\) flexible multi-structures.
• Asymptotic behavior of some elastic planar networks of Bernoulli–Euler beams
• On the Modelling and Exact Controllability of Networks of Vibrating Strings
• Stabilization of second order evolution equations by a class of unbounded feedbacks
• Fourier Series in Control Theory

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