Stability of Timoshenko systems with past history

We consider vibrating systems of Timoshenko type with past history acting only in one equation. We show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds. Otherwise the corresponding system does not...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 339; no. 1; pp. 482 - 502
Main Authors MUNOZ RIVERA, Jaime E, FERNANDEZ SARE, Hugo D
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.03.2008
Elsevier
Subjects
Exact sciences and technology
Exponential stability
Mathematical analysis
Mathematics
Partial differential equations
Polynomial rate of decay
Sciences and techniques of general use
Timoshenko system
Exponential stability
Timoshenko system
Polynomial rate of decay
Wave equation
Polynomial
Mathematical analysis
Solution decay
Regularity
Numerical stability
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Summary:We consider vibrating systems of Timoshenko type with past history acting only in one equation. We show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds. Otherwise the corresponding system does not decay exponentially as time goes to infinity. In the case that the wave speeds of the equations are different, which is more realistic from the physical point of view, we show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.07.012