Electron. J. Diff. Equ., Vol. 2013 (2013), No. 01, pp. 1-17.

Behavior of the energy for Lame systems in bounded domains with nonlinear damping and external force

Ahmed Bchatnia, Moez Daoulatli

We study behavior of the energy for solutions to a Lame system on a bounded domain, with localized nonlinear damping and external force. The equation is set up in three dimensions and under a microlocal geometric condition. More precisely, we prove that the behavior of the energy is determined by a solution to a forced differential equation, an it depends on the L^2 norm of the force.

Submitted November 8, 2012. Published January 7, 2013
Math Subject Classifications: 35L05, 35B40.
Key Words: Lame system; nonlinear damping; bounded domain; external force

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Ahmed Bchatnia
Department of Mathematics, Faculty of Sciences of Tunis
University of Tunis El Manar, Campus Universitaire 2092
- El Manar 2, Tunis, Tunisia
email: ahmed.bchatnia@fst.rnu.tn
Moez Daoulatli
Department of Mathematics, Faculty of Sciences of Bizerte
University of Carthage
7021, Jarzouna, Bizerte, Tunisia

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