Rates of decay to weak thermoelastic Bresse system

We consider the Bresse system with temperature and we show that there exist exponential stability if and only if the wave propagation is equal. We show that, in general, the system is not exponentially stable but that there exists polynomial stability with rates that depend on the wave propagations...

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Bibliographic Details
Published in:IMA journal of applied mathematics 2010-12, Vol.75 (6), p.881-904
Main Authors: HARUE FATORI, Luci, MUNOZ RIVERA, Jaime E
Format: Article
Language:English
Subjects:
Bresse thermoelastic systems
Decay
Decay rate
Dissipation
Exact sciences and technology
Mathematical analysis
Mathematics
Optimization
polynomial stability
Regularity
Sciences and techniques of general use
Stability
thermoelasticity decay rate
Wave propagation
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Summary:We consider the Bresse system with temperature and we show that there exist exponential stability if and only if the wave propagation is equal. We show that, in general, the system is not exponentially stable but that there exists polynomial stability with rates that depend on the wave propagations and the regularity of the initial data. Moreover, we introduce a necessary condition to dissipative semigroup decay polynomially. This result allows us to show some optimality to the polynomial rate of decay.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxq038