|
Stabilization of a system of anisotropic thermoelasticity by nonlinear boundary and internal feedbacks
Author(s):
Amar
Heminna;
Serge
Nicaise;
Abdoulaye
Sène
Journal:
Quart. Appl. Math.
63
(2005),
429-453.
MSC (2000):
Primary 35B35, 73B30
Posted:
July 11, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We consider the stabilization of an anisotropic thermoelasticity system with a natural Neumann boundary condition on part of the boundary and combined nonlinear internal and boundary feedbacks. We then give an answer to a problem raised by Liu and Zuazua.
References:
-
- 1.
- BEY, R.; HEMINNA, A.; LOHEAC, J.-P., Boundary stabilization of a linear elastodynamic system with variable coefficients, E.J.D.E. 2001 (2001), Num. 78, 1-23. MR 1872057 (2002h:93089)
- 2.
- BROSSARD, R.; LOHEAC, J.-P., Stabilisation frontière du système élastodynamique dans un polygone plan, C. R. Acad. Sci. Math. 338 (2004), 213-218. MR 2038326 (2004k:93068)
- 3.
- ELLER, M.; LAGNESE, J.E.; NICAISE, S., Decay rates for solutions of a Maxwell system with nonlinear boundary damping, Comp. and Appl. Math., 21 (2002), 135-165. MR 2009950 (2004i:78006)
- 4.
- GUESMIA, A., Existence globale and stabilisation frontière non linéaire d'un système d'élasticité, Portugaliae Mathematica, 56 (1999), 361-379. MR 1716059 (2001k:74073)
- 5.
- HANSEN, S.W., Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl. 167 (1992), 429-442. MR 1168599 (93f:35229)
- 6.
- HEMINNA, A.; NICAISE, S.; SENE A., Stabilisation d'un système de la thermoélasticité avec feebacks non linéaires, C.R. Acad. Sci. Paris, série I Math. 339 (2004), 561-566. MR 2111352
- 7.
- HORN, M.A., Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity, J. Math. Anal. Appl. 223 (1998), 126-50. MR 1627344 (99c:93059)
- 8.
- KOMORNIK, V., Exact Controllability And Stabilization, The Multiplier Method, RMA 36, Masson, 1994. MR 1359765 (96m:93003)
- 9.
- LEMRABET, K., Étude de divers problèmes aux limites de Ventcel d'origine physique ou mécanique dans des domaines non réguliers, Thesis, U.S.T.H.B., Alger, 1987.
- 10.
- NARUKAWA, K., Boundary value control of thermoelastic systems, Hiroshima Math. J. 13 (1983), 227-272. MR 0707182 (85c:93021)
- 11.
- NICAISE, S.; SENE, A., Stabilisation non linéaire d'un système de la thermoélasticité isotrope, Preprint MACS 03-12, 2003.
- 12.
- NICAISE, S., Stability and controllability of the electromagneto-elastic system, Portugaliae Mathematica 60 (2003), 37-70. MR 1961551 (2003m:93008)
- 13.
- NICAISE, S., Stability and controllability of and abstract evolution equation of hyperbolic type and concrete applications, Rendiconti di Matematica, Serie VII, 23 (2003), 83-116. MR 2044992 (2005a:93024)
- 14.
- LEBEAU, G.; ZUAZUA, E., Decay rates for the three-dimensional linear system of thermoelasticity, Arch. Rat. Mech. Anal. 148 (1999) 179-231. MR 1716306 (2000h:35154)
- 15.
- LIU, W.J., Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity, ESAIM COCV 3 (1998), 23-48. MR 1610226 (99i:93056a)
- 16.
- LIU, W.J.; ZUAZUA.E., Uniform stabilization of the higher-dimensional system of thermoelasticity with a nonlinear boundary feedback, Quarterly of Applied Mathematics 59 (2001), 269-314. MR 1828455 (2002d:74018)
- 17.
- LIU, Z.; ZHENG, S., Exponential stability of the semigroup associated with a thermoelastic system, Quart. Appl. Math. 51 (1993), 535-545. MR 1233528 (95c:35247)
- 18.
- MUÑOZ RIVERA, J.E., Decomposition of the displacement vector field and decay rates in linear thermoelasticity, SIAM J. Math. Anal. 24 (1993), 390-406. MR 1205533 (94a:73007)
- 19.
- MUÑOZ RIVERA, J.E., Asymptotic behaviour in n-dimensional thermoelasticity, Appl. Math. Lett. 10 (1997), 47-53. MR 1471316 (98j:73016)
- 20.
- OLIVEIRA, L.A.F., Exponential decay in thermoelasticity, Commun. Appl. Anal. 1 (1997), 113-118. MR 1453945 (98d:73011)
- 21.
- SHOWALTER, R.E., Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Math. Surveys and Monographs, 49, AMS, 1997. MR 1422252 (98c:47076)
- 22.
- VALID, R., La mécanique des milieux continus et le calcul des structures, Eyrolles, Paris, 1977.
Similar Articles:
Retrieve articles in Quarterly of Applied Mathematics
with MSC
(2000):
35B35, 73B30
Retrieve articles in all Journals with MSC
(2000):
35B35, 73B30
Additional Information:
Amar
Heminna
Affiliation:
U.S.T.H.B., Fac de Maths, El-Alia, Bab Ezzouar, Alger Algérie
Email:
ahemina@hotmail.com
Serge
Nicaise
Affiliation:
Université de Valenciennes et du Hainaut-Cambrésis, MACS, Institut des Sciences et Techniques de Valenciennes, F-59313 Valenciennes Cedex 9, France
Email:
s.nicaise@univ-valenciennes.fr
Abdoulaye
Sène
Affiliation:
Université Cheikh Anta DIOP, Département de Mathématiques, Faculté des sciences et techniques, Dakar Sénégal
Email:
abdousen@ucad.sn
PII:
S0033-569X-05-00967-4
Received by editor(s):
February 1, 2004
Posted:
July 11, 2005
Copyright of article:
Copyright
2005,
Brown University
|