Abstract
We perform a spectral analysis of abstract thermo-elastic plate equations with ‘hinged’ B.C. in the presence of rotational forces, whereby the elastic equation is the (hyperbolic) Kirchoff equation. A precise description is given, which in particular shows that the resulting s.c. semi-group of contractions is neither compact nor differentiable for t > 0 (it contains an infinite-dimensional group invariant component). This is in sharp contrast with the case where rotational forces are neglected, whereby the elastic equation is the Euler-Bernoulli equation: in this latter case, the semigroup is, instead, analytic, under all canonical sets of B.C.
This research was partially supported by Yeungnam University and by TGRC, in addition to being partially supported by the National Science Foundation under Grant DMS-9504822, and by the Army Research Office under Grant DAAH04-96-1-0059.
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References
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Chang, S.K., Triggiani, R. (1998). Spectral Analysis of Thermo-elastic Plates with Rotational Forces. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_5
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_5
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