## Stability of the Timoshenko system and a Lagnese-Lions’ conjecture

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In 1988 Lagnese-Lions conjectured that the asymptotic limit of Timoshenko system converges to the Von-Kármán system. In the last years a series of papers related to this conjecture have been published and although they have been achieved several advances, so far we just have partial answers to this problem. The aim of this talk is to give a definitive answer for the Lagnese-Lions conjecture and to answer others important questions about asymptotic limit and stability for the Timoshenko system by generalizing some results (due to Lagnese and Lions on the one hand, and to Araruna and Zuazua on the other). I will present results of a joint work with F. Araruna and P. Braz e Silva, and results of a joint work with F. Ammar-Khodja.