Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 344, Issue 2, Pages 75-96Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2005.10.003
Keywords
thermoelastic system; Riesz basis; stability; partial differential equation system
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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. (C) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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