Global existence and energy decay of solutions to a Bresse system with delay terms

Abbes Benaissa; Mostefa Miloudi; Mokhtar Mokhtari

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 2, page 169-186
  • ISSN: 0010-2628

Abstract

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We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.

How to cite

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Benaissa, Abbes, Miloudi, Mostefa, and Mokhtari, Mokhtar. "Global existence and energy decay of solutions to a Bresse system with delay terms." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 169-186. <http://eudml.org/doc/270113>.

@article{Benaissa2015,
abstract = {We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.},
author = {Benaissa, Abbes, Miloudi, Mostefa, Mokhtari, Mokhtar},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Bresse system; delay terms; decay rate; multiplier method; Bresse system; delay term; exponential decay; initial boundary value problem; multiplier method; semigroup},
language = {eng},
number = {2},
pages = {169-186},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Global existence and energy decay of solutions to a Bresse system with delay terms},
url = {http://eudml.org/doc/270113},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Benaissa, Abbes
AU - Miloudi, Mostefa
AU - Mokhtari, Mokhtar
TI - Global existence and energy decay of solutions to a Bresse system with delay terms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 169
EP - 186
AB - We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.
LA - eng
KW - Bresse system; delay terms; decay rate; multiplier method; Bresse system; delay term; exponential decay; initial boundary value problem; multiplier method; semigroup
UR - http://eudml.org/doc/270113
ER -

References

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  1. Bresse J.A.C., Cours de Méchanique Appliquée, Mallet Bachelier, Paris, 1859. 
  2. Kim J.U., Renardy Y., 10.1137/0325078, SIAM J. Control Optim. 25 (1987), 1417–1429. Zbl0632.93057MR0912448DOI10.1137/0325078
  3. Messaoudi S.A., Mustapha M.I., 10.1007/s00030-008-7075-3, Nonlinear Differ. Equ. Appl. 15 (2008), 655–671. MR2465776DOI10.1007/s00030-008-7075-3
  4. Messaoudi S.A., Mustapha M.I., 10.1002/mma.1047, Math. Meth. Appl. Sci. 32 (2009), 454–469. MR2493590DOI10.1002/mma.1047
  5. Park J.H., Kang J.R., 10.1093/imamat/hxq040, IMA J. Appl. Math. 76 (2011), 340–350. Zbl1219.35311MR2781698DOI10.1093/imamat/hxq040
  6. Raposo C.A., Ferreira J., Santos J., Castro N.N.O., 10.1016/j.aml.2004.03.017, Appl. Math. Lett. 18 (2005), no. 5, 535–541. Zbl1072.74033MR2127817DOI10.1016/j.aml.2004.03.017
  7. Liu Z., Rao B., 10.1007/s00033-008-6122-6, Z. Angew. Math. Phys. 60 (2009), 54–69. Zbl1161.74030MR2469727DOI10.1007/s00033-008-6122-6
  8. Shinskey F.G., Process Control Systems, McGraw-Hill Book Company, New York, 1967. 
  9. Abdallah C., Dorato P., Benitez-Read J., Byrne R., Delayed Positive Feedback Can Stabilize Oscillatory System, ACC, San Francisco, (1993), 3106–3107. 
  10. Suh I.H., Bien Z., 10.1109/TAC.1980.1102347, IEEE Trans. Autom. Control 25 (1980), 600–603. DOI10.1109/TAC.1980.1102347
  11. Datko R., Lagnese J., Polis M.P., 10.1137/0324007, SIAM J. Control Optim. 24 (1986), 152–156. Zbl0592.93047MR0818942DOI10.1137/0324007
  12. Nicaise S., Pignotti C., 10.1137/060648891, SIAM J. Control Optim. 45 (2006), no. 5, 1561–1585. Zbl1180.35095MR2272156DOI10.1137/060648891
  13. Xu C.Q., Yung S.P., Li L.K., 10.1051/cocv:2006021, ESAIM Control Optim. Calc. Var. 12 (2006), 770–785. MR2266817DOI10.1051/cocv:2006021
  14. Brézis H., Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Notas de Matemática (50), Universidade Federal do Rio de Janeiro and University of Rochester, North-Holland, Amsterdam, 1973. Zbl0252.47055MR0348562
  15. Haraux A., Two remarks on hyperbolic dissipative problems, Res. Notes in Math. 122, Pitman, Boston, MA, 1985, pp. 161–179. Zbl0579.35057MR0879461
  16. Komornik V., Exact Controllability and Stabilization. The Multiplier Method, Masson-John Wiley, Paris, 1994. Zbl0937.93003MR1359765

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