Stabilization of a system of anisotropic thermoelasticity by nonlinear boundary and internal feedbacks
Authors:
Amar Heminna, Serge Nicaise and Abdoulaye Sène
Journal:
Quart. Appl. Math. 63 (2005), 429-453
MSC (2000):
Primary 35B35, 73B30
DOI:
https://doi.org/10.1090/S0033-569X-05-00967-4
Published electronically:
July 11, 2005
MathSciNet review:
2169027
Full-text PDF Free Access
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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.
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he 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.
loheac BROSSARD, R.; LOHEAC, J.-P., Stabilisation frontière du système élastodynamique dans un polygone plan, C. R. Acad. Sci. Math. 338 (2004), 213-218.
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gues GUESMIA, A., Existence globale and stabilisation frontière non linéaire d’un système d’élasticité, Portugaliae Mathematica, 56 (1999), 361-379.
zl17 HANSEN, S.W., Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl. 167 (1992), 429-442.
he1 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.
ho 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.
vk KOMORNIK, V., Exact Controllability And Stabilization, The Multiplier Method, RMA 36, Masson, 1994.
le 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.
l40 NARUKAWA, K., Boundary value control of thermoelastic systems, Hiroshima Math. J. 13 (1983), 227-272.
sn NICAISE, S.; SENE, A., Stabilisation non linéaire d’un système de la thermoélasticité isotrope, Preprint MACS 03-12, 2003.
sn1 NICAISE, S., Stability and controllability of the electromagneto-elastic system, Portugaliae Mathematica 60 (2003), 37-70.
sn2 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.
lz LEBEAU, G.; ZUAZUA, E., Decay rates for the three-dimensional linear system of thermoelasticity, Arch. Rat. Mech. Anal. 148 (1999) 179–231.
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zl47 OLIVEIRA, L.A.F., Exponential decay in thermoelasticity, Commun. Appl. Anal. 1 (1997), 113-118.
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va VALID, R., La mécanique des milieux continus et le calcul des structures, Eyrolles, Paris, 1977.
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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
Received by editor(s):
February 1, 2004
Published electronically:
July 11, 2005
Article copyright:
© Copyright 2005
Brown University