Optimal Control pp 84-115 | Cite as

# Spectral Analysis of Thermo-elastic Plates with Rotational Forces

## 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.

## Keywords

Spectral Analysis Contraction Semigroup Bounded Perturbation Rotational Force Complex Conjugate Root## Preview

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