Abstract
In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the L2-norm of the solution and its higher order derivatives. In fact, if we consider just one damping term acting on the second equation of the solution, we show that the solution does not decay at all. On the other hand, by considering one damping term alone acting on the third equation, we show that this damping term is strong enough to stabilize the whole system. In this case, we found a completely new stability number that depends on the parameters in the system. In addition, we prove the optimality of the results by using eigenvalues expansions. We have also improved the result obtained recently in [12] for the two damping terms case and get better decay estimates. Our obtained results have been proved under some assumptions on the wave speeds of the three equations in the Bresse system.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1870-1898 |
| Number of pages | 29 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 455 |
| Issue number | 2 |
| DOIs | |
| State | Published - Nov 15 2017 |
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Keywords
- Bresse system
- Decay rate
- Regularity loos
- Timoshenko system
- Wave speeds
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
On the stability of the Bresse system with frictional damping. / Ghoul, Tej-eddine; Khenissi, Moez; Said-Houari, Belkacem.
In: Journal of Mathematical Analysis and Applications, Vol. 455, No. 2, 15.11.2017, p. 1870-1898.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the stability of the Bresse system with frictional damping
AU - Ghoul, Tej-eddine
AU - Khenissi, Moez
AU - Said-Houari, Belkacem
PY - 2017/11/15
Y1 - 2017/11/15
N2 - In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the L2-norm of the solution and its higher order derivatives. In fact, if we consider just one damping term acting on the second equation of the solution, we show that the solution does not decay at all. On the other hand, by considering one damping term alone acting on the third equation, we show that this damping term is strong enough to stabilize the whole system. In this case, we found a completely new stability number that depends on the parameters in the system. In addition, we prove the optimality of the results by using eigenvalues expansions. We have also improved the result obtained recently in [12] for the two damping terms case and get better decay estimates. Our obtained results have been proved under some assumptions on the wave speeds of the three equations in the Bresse system.
AB - In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the L2-norm of the solution and its higher order derivatives. In fact, if we consider just one damping term acting on the second equation of the solution, we show that the solution does not decay at all. On the other hand, by considering one damping term alone acting on the third equation, we show that this damping term is strong enough to stabilize the whole system. In this case, we found a completely new stability number that depends on the parameters in the system. In addition, we prove the optimality of the results by using eigenvalues expansions. We have also improved the result obtained recently in [12] for the two damping terms case and get better decay estimates. Our obtained results have been proved under some assumptions on the wave speeds of the three equations in the Bresse system.
KW - Bresse system
KW - Decay rate
KW - Regularity loos
KW - Timoshenko system
KW - Wave speeds
UR - http://www.scopus.com/inward/record.url?scp=85021825750&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85021825750&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2017.04.027
DO - 10.1016/j.jmaa.2017.04.027
M3 - Article
AN - SCOPUS:85021825750
VL - 455
SP - 1870
EP - 1898
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -