Strong asymptotic stability for n-dimensional thermoelasticity systems

Mohammed Aassila

Colloquium Mathematicae (1998)

  • Volume: 77, Issue: 1, page 133-139
  • ISSN: 0010-1354

Abstract

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We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.

How to cite

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Aassila, Mohammed. "Strong asymptotic stability for n-dimensional thermoelasticity systems." Colloquium Mathematicae 77.1 (1998): 133-139. <http://eudml.org/doc/210571>.

@article{Aassila1998,
abstract = {We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.},
author = {Aassila, Mohammed},
journal = {Colloquium Mathematicae},
keywords = {no growth assumption at the origin; lack of compactness},
language = {eng},
number = {1},
pages = {133-139},
title = {Strong asymptotic stability for n-dimensional thermoelasticity systems},
url = {http://eudml.org/doc/210571},
volume = {77},
year = {1998},
}

TY - JOUR
AU - Aassila, Mohammed
TI - Strong asymptotic stability for n-dimensional thermoelasticity systems
JO - Colloquium Mathematicae
PY - 1998
VL - 77
IS - 1
SP - 133
EP - 139
AB - We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.
LA - eng
KW - no growth assumption at the origin; lack of compactness
UR - http://eudml.org/doc/210571
ER -

References

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  1. [1] Aassila M., Nouvelle approche à la stabilisation forte des systèmes distribués, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), 43-48. 
  2. [2] Aassila M. , A new approach to strong stabilization of distributed systems, Differential Integral Equations, to appear. 
  3. [3] Aassila M. , Strong asymptotic stability of isotropic elasticity systems with internal damping, Acta Sci. Math. (Szeged) 64 (1998), 3-8. Zbl0907.35016
  4. [4] Ball J. M., On the asymptotic behavior of generalized processes with applications to nonlinear evolution equations, J. Differential Equations 27 (1978), 224-265. Zbl0376.35002
  5. [5] Dafermos C. M., On the existence and asymptotic stability of solutions of the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29 (1968), 241-271. Zbl0183.37701
  6. [6] R. Dautray et J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 1, Masson, 1987. Zbl0708.35003
  7. [7] Muñoz Rivera J. E., Energy decay rates in linear thermoelasticity, Funkcial. Ekvac. 35 (1992), 19-30. Zbl0838.73006
  8. [11] Ouazza M., Estimation d'énergie et résultats de contrôlabilité pour certains systèmes couplés, PhD thesis, Université de Strasbourg, June 1996. 
  9. [12] Slemrod M., Global existence, uniqueness and asymptotic stability of classical smooth solutions in one dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal. 76 (1981), 97-133. Zbl0481.73009

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