Abstract
In this paper, we study the Riesz basis property of the generalized eigenfunctions of a one-dimensional hyperbolic system in the energy state space. This characterizes the dynamic behavior of the system, particularly the stability, in terms of its eigenfrequencies. This system is derived from a thermoelastic equation with memory type. The asymptotic expansions for eigenvalues and eigenfunctions are developed. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the C 0 -semigroup associated with the system, and as a consequence, the exponential stability of the system is concluded.
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