Stability and optimality of decay rate for a weakly dissipative Bresse system

This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the la...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2015-03, Vol.38 (5), p.898-908
Main Authors: Alves, M.O., Fatori, L.H., Jorge Silva, M.A., Monteiro, R.N.
Format: Article
Language:English
Subjects:
Asymptotic properties
Bresse system
Decay
Decay rate
Dissipation
exponential stability
Mathematical analysis
optimality
Optimization
polynomial stability
Polynomials
Stability
Wave propagation
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Summary:This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3115