Asymptotic Behavior of the Eigenfrequency of a One-Dimensional Linear Thermoelastic System*

In this paper, we are concerned with the asymptotic behavior of the eigenvalues arising from a one-dimensional linear thermoelastic system with the Dirichlet] Dirichlet boundary condition. It is shown that the eigenfrequency asymptotically falls on two branches: one branch is along the negative horizontal axis in the complex plane and the other branch is asymptotic to the vertical line Rel s yg 2r2 k. These results lead to the exponential stability of the system and also provide a proof for the numerical simulation results by Liu and Zheng 1993, Quart. Appl. Math., 51, 535]545..