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Stability and optimality of decay rate for a weakly dissipative Bresse system
Author(s) -
Alves M.O.,
Fatori L.H.,
Jorge Silva M.A.,
Monteiro R.N.
Publication year - 2014
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.3115
Subject(s) - dissipative system , exponential stability , mathematics , exponential growth , stability (learning theory) , operator (biology) , zero (linguistics) , mathematical analysis , polynomial , exponential decay , control theory (sociology) , physics , computer science , thermodynamics , nonlinear system , quantum mechanics , control (management) , machine learning , artificial intelligence , biochemistry , chemistry , linguistics , philosophy , repressor , transcription factor , gene
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.