Electron. J. Diff. Equ., Vol. 2014 (2014), No. 182, pp. 1-19.

Weakly locally thermal stabilization of Bresse systems

Nadine Najdi, Ali Wehbe

Fatori and Rivera [7] studied the stability of the Bresse system with one distributed temperature dissipation law operating on the angle displacement equation. They proved that, in general, the energy of the system does not decay exponentially and they established the rate of $t^{-1/3}$. In this article, our goal is to extend their results, by taking into consideration the important case when the thermal dissipation is locally distributed and to improve the polynomial energy decay rate. We then study the energy decay rate of Bresse system with one locally thermal dissipation law. Under the equal speed wave propagation condition, we establish an exponential energy decay rate. On the contrary, we prove that the energy of the system decays, in general, at the rate $t^{-1/2}$.

Submitted May 6, 2014. Published August 27, 2014.
Math Subject Classifications: 35B37, 35D05, 93C20, 73K50.
Key Words: Thermoelastic Bresse system; locally damping; strong stability; exponential stability; polynomial stability; frequency domain method; piece wise multiplier method.

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Nadine Najdi
Université de Valenciennes et du Hainaut Cambrésis
59313 Valenciennes Cedex 9, France
email: nadine.najdi@etu.univ-valenciennes.fr
Ali Wehbe
Lebanese University, Faculty of sciences I
Hadath-Beirut, Lebanon
email: ali.wehbe@ul.edu.lb

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