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Title Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same

Name Belkacem Said Houari
Country United Arab Emirates
Email saidhouarib@yahoo.fr
Co-Author(s) Aslan Kasimov
Submit Time 2014-02-25 11:12:59
Special Session 60: Recent advances in evolutionary equations
We consider the Cauchy problem for the one-dimensional Timoshenko system coupled with heat conduction, wherein the latter is described by either the Cattaneo law or the Fourier law. We prove that heat dissipation alone is sufficient to stabilize the system in both cases, so that additional mechanical damping is unnecessary. However, the decay of solutions without the mechanical damping is found to be slower than that with mechanical damping. Furthermore, in contrast to earlier results, we find that the Timoshenko Fourier and the Timoshenko Cattaneo systems have the same decay rate. The rate depends on a certain number, which is a function of the parameters of the system.