## Preprint 2016-28

## Luci Fatori, Tais De Olivera Saito, Mauricio Sepúlveda, Eiji Renan Takahashi:

### Energy decay to Timoshenko system with indefinite damping

### Abstract:

We consider the classical Timoshenko system for vibrations of thin rods. The system has an indenite damping mechanism, i.e. it has a damping function a = a(x) possibly changing sign, present only in the equation for the vertical displacement. We shall prove that exponential stability depends on conditions regarding of the indenite damping function a and a nice relationship between the coecient of the system. Finally, we give some numerical result to verify our analytical results.

This preprint gave rise to the following definitive publication(s):

**Luci FATORI, Tais De Olivera SAITO, Mauricio SEPúLVEDA, Eiji Renan TAKAHASHI: ***Energy decay to Timoshenko system with indefinite damping*. Mathematical Methods in the Applied Sciences, vol. 43, 1, pp. 225-241, (2020).