Exponential stability of the semigroup associated with a thermoelastic system

Liu, Zhuangyi; Zheng, Song Mu

doi:10.1090/qam/1233528

Authors: Zhuangyi Liu and Song Mu Zheng
Journal: Quart. Appl. Math. 51 (1993), 535-545
MSC: Primary 35Q72; Secondary 34G10, 47N20, 73B30, 93C25
DOI: https://doi.org/10.1090/qam/1233528
MathSciNet review: MR1233528
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Abstract: In this paper it is proved that the semigroup associated with the one-dimensional thermoelastic system with Dirichlet boundary conditions is an exponentially stable ${C_0}$-semigroup of contraction on the space $H_0^1 \times {L^2} \times {L^2}$. The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in $D\left ( A \right )$ recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-Quadratic-Gaussian optimal control problem is also discussed.

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