Electron. J. Diff. Equ., Vol. 2014 (2014), No. 254, pp. 1-15.

Well-posedness and exponential stability for a linear damped Timoshenko system with second sound and internal distributed delay

Tijani A. Apalara

In this article we consider one-dimensional linear thermoelastic system of Timoshenko type with linear frictional damping and a distributed delay acting on the displacement equation. The heat flux of the system is governed by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we establish the well-posedness result and prove that the system is exponentially stable regardless of the speeds of wave propagation.

Submitted August 10, 2014. Published December 4, 2014.
Math Subject Classifications: 35B40, 74F05, 74F20, 93D15, 93D20.
Key Words: Timoshenko system; second sound well-posedness; exponential stability; distributed delay.

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Tijani A. Apalara
Affiliated Colleges at Hafr Al-Batin
General Science and Studies Unit-Mathematics
King Fahd University of Petroleum and Minerals
Hafr Al-Batin 31991, Saudi Arabia
email: tijani@kfupm.edu.sa

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