Stability analysis of a thermo-elastic system of type II with boundary viscoelastic damping

摘要

The stability of a kind of one-dimensional thermo-elastic system of type II is considered. This system consists of two strongly coupled wave equations. Suppose that there exists an viscoelastic damping at one end of the 1-d domain. If without coupling, this damping always makes one of these two wave equations (the corresponding pure elastic system) achieve exponential stability and the other wave system (heat equation of type II) be conservative. Whether the coupling can pass the damping effect from the dissipative elastic system to the conservative heat system of type II is discussed. However, by a detailed spectral analysis, it is proved that this thermo-elastic system is at most asymptotically stable but not exponentially stable. A numerical simulation is given to support these results obtained in this paper.