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Polynomial and analytic stabilization of a wave equation coupled with an Euler–Bernoulli beam
Author(s) -
Ammari Kaïs,
Nicaise Serge
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1052
Subject(s) - mathematics , polynomial , euler's formula , stability (learning theory) , bernoulli's principle , routh–hurwitz stability criterion , exponential stability , mathematical analysis , exponential function , nonlinear system , physics , quantum mechanics , machine learning , computer science , engineering , aerospace engineering
We consider a stabilization problem for a model arising in the control of noise. We prove that in the case where the control zone does not satisfy the geometric control condition, B.L.R. (see Bardos et al. SIAM J. Control Optim. 1992; 30 :1024–1065), we have a polynomial stability result for all regular initial data. Moreover, we give a precise estimate on the analyticity of reachable functions where we have an exponential stability. Copyright © 2008 John Wiley & Sons, Ltd.