Strong asymptotic stability for n-dimensional thermoelasticity systems

• Autorzy: Mohammed Aassila
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 77
• Numer: 1
• Strony: 133-139

Daty

wydano

1998

otrzymano

1997-05-12

poprawiono

1997-12-01

Twórcy

autor

Mohammed Aassila

• Département de Mathématique, Université Louis Pasteur 7, rue René Descartes 67084 Strasbourg Cedex, France

Bibliografia

• [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] Aassila M. , A new approach to strong stabilization of distributed systems, Differential Integral Equations, to appear.
• [3] Aassila M. , Strong asymptotic stability of isotropic elasticity systems with internal damping, Acta Sci. Math. (Szeged) 64 (1998), 3-8.
• [4] Ball J. M., On the asymptotic behavior of generalized processes with applications to nonlinear evolution equations, J. Differential Equations 27 (1978), 224-265.
• [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.
• [6] R. Dautray et J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 1, Masson, 1987.
• [7] Muñoz Rivera J. E., Energy decay rates in linear thermoelasticity, Funkcial. Ekvac. 35 (1992), 19-30.
• [11] Ouazza M., Estimation d'énergie et résultats de contrôlabilité pour certains systèmes couplés, PhD thesis, Université de Strasbourg, June 1996.
• [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.